df673cad4e
* solvers -> solver * adaptive_functions -> adaptive_function * callbacks -> callback * operators -> operator * pinns -> physics_informed_solver * layers -> block
504 lines
19 KiB
Python
504 lines
19 KiB
Python
""" Module for adaptive functions. """
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import torch
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from ..utils import check_consistency
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from .adaptive_func_interface import AdaptiveActivationFunctionInterface
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class AdaptiveReLU(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.ReLU` activation function.
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Given the function :math:`\text{ReLU}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{ReLU}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{ReLU}_{\text{adaptive}}({x}) = \alpha\,\text{ReLU}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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ReLU function is defined as:
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.. math::
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\text{ReLU}(x) = \max(0, x)
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
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knowledge engineering and knowledge management (IC3K).
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Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
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<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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activation functions accelerate convergence in deep and
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physics-informed neural networks*. Journal of
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Computational Physics 404 (2020): 109136.
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DOI: `JCP 10.1016
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<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.ReLU()
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class AdaptiveSigmoid(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.Sigmoid` activation function.
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Given the function :math:`\text{Sigmoid}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{Sigmoid}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{Sigmoid}_{\text{adaptive}}({x}) = \alpha\,\text{Sigmoid}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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Sigmoid function is defined as:
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.. math::
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\text{Sigmoid}(x) = \frac{1}{1 + \exp(-x)}
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
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knowledge engineering and knowledge management (IC3K).
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Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
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<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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activation functions accelerate convergence in deep and
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physics-informed neural networks*. Journal of
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Computational Physics 404 (2020): 109136.
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DOI: `JCP 10.1016
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<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.Sigmoid()
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class AdaptiveTanh(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.Tanh` activation function.
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Given the function :math:`\text{Tanh}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{Tanh}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{Tanh}_{\text{adaptive}}({x}) = \alpha\,\text{Tanh}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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Tanh function is defined as:
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.. math::
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\text{Tanh}(x) = \frac{\exp(x) - \exp(-x)} {\exp(x) + \exp(-x)}
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
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knowledge engineering and knowledge management (IC3K).
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Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
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<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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activation functions accelerate convergence in deep and
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physics-informed neural networks*. Journal of
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Computational Physics 404 (2020): 109136.
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DOI: `JCP 10.1016
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<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.Tanh()
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class AdaptiveSiLU(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.SiLU` activation function.
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Given the function :math:`\text{SiLU}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{SiLU}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{SiLU}_{\text{adaptive}}({x}) = \alpha\,\text{SiLU}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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SiLU function is defined as:
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.. math::
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\text{SiLU}(x) = x * \sigma(x), \text{where }\sigma(x)
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\text{ is the logistic sigmoid.}
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
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knowledge engineering and knowledge management (IC3K).
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Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
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<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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activation functions accelerate convergence in deep and
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physics-informed neural networks*. Journal of
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Computational Physics 404 (2020): 109136.
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DOI: `JCP 10.1016
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<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.SiLU()
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class AdaptiveMish(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.Mish` activation function.
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Given the function :math:`\text{Mish}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{Mish}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{Mish}_{\text{adaptive}}({x}) = \alpha\,\text{Mish}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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Mish function is defined as:
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.. math::
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\text{Mish}(x) = x * \text{Tanh}(x)
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
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knowledge engineering and knowledge management (IC3K).
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Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
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<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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activation functions accelerate convergence in deep and
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physics-informed neural networks*. Journal of
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Computational Physics 404 (2020): 109136.
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DOI: `JCP 10.1016
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<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.Mish()
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class AdaptiveELU(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.ELU` activation function.
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Given the function :math:`\text{ELU}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{ELU}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{ELU}_{\text{adaptive}}({x}) = \alpha\,\text{ELU}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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ELU function is defined as:
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.. math::
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\text{ELU}(x) = \begin{cases}
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x, & \text{ if }x > 0\\
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\exp(x) - 1, & \text{ if }x \leq 0
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\end{cases}
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
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knowledge engineering and knowledge management (IC3K).
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Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
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<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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activation functions accelerate convergence in deep and
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physics-informed neural networks*. Journal of
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Computational Physics 404 (2020): 109136.
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DOI: `JCP 10.1016
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<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.ELU()
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class AdaptiveCELU(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.CELU` activation function.
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Given the function :math:`\text{CELU}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{CELU}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{CELU}_{\text{adaptive}}({x}) = \alpha\,\text{CELU}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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CELU function is defined as:
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.. math::
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\text{CELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x) - 1))
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
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knowledge engineering and knowledge management (IC3K).
|
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Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
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<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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activation functions accelerate convergence in deep and
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physics-informed neural networks*. Journal of
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Computational Physics 404 (2020): 109136.
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DOI: `JCP 10.1016
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<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.CELU()
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class AdaptiveGELU(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.GELU` activation function.
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Given the function :math:`\text{GELU}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{GELU}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{GELU}_{\text{adaptive}}({x}) = \alpha\,\text{GELU}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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GELU function is defined as:
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.. math::
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\text{GELU}(x) = 0.5 * x * (1 + \text{Tanh}(\sqrt{2 / \pi} * (x + 0.044715 * x^3)))
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
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knowledge engineering and knowledge management (IC3K).
|
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Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
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<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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activation functions accelerate convergence in deep and
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physics-informed neural networks*. Journal of
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Computational Physics 404 (2020): 109136.
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DOI: `JCP 10.1016
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<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.GELU()
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class AdaptiveSoftmin(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.Softmin` activation function.
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Given the function :math:`\text{Softmin}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{Softmin}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{Softmin}_{\text{adaptive}}({x}) = \alpha\,\text{Softmin}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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Softmin function is defined as:
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.. math::
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\text{Softmin}(x_{i}) = \frac{\exp(-x_i)}{\sum_j \exp(-x_j)}
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
|
|
knowledge engineering and knowledge management (IC3K).
|
|
Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
|
|
<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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|
activation functions accelerate convergence in deep and
|
|
physics-informed neural networks*. Journal of
|
|
Computational Physics 404 (2020): 109136.
|
|
DOI: `JCP 10.1016
|
|
<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.Softmin()
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class AdaptiveSoftmax(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :class:`~torch.nn.Softmax` activation function.
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Given the function :math:`\text{Softmax}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{Softmax}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{Softmax}_{\text{adaptive}}({x}) = \alpha\,\text{Softmax}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters, and the
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Softmax function is defined as:
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.. math::
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\text{Softmax}(x_{i}) = \frac{\exp(x_i)}{\sum_j \exp(x_j)}
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
|
|
and its potential to improve generalization in neural networks.*
|
|
2015 7th international joint conference on knowledge discovery,
|
|
knowledge engineering and knowledge management (IC3K).
|
|
Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
|
|
<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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|
activation functions accelerate convergence in deep and
|
|
physics-informed neural networks*. Journal of
|
|
Computational Physics 404 (2020): 109136.
|
|
DOI: `JCP 10.1016
|
|
<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.nn.Softmax()
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class AdaptiveSIREN(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :obj:`~torch.sin` function.
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Given the function :math:`\text{sin}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{sin}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{sin}_{\text{adaptive}}({x}) = \alpha\,\text{sin}(\beta{x}+\gamma),
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where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters.
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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|
*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
|
|
2015 7th international joint conference on knowledge discovery,
|
|
knowledge engineering and knowledge management (IC3K).
|
|
Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
|
|
<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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|
activation functions accelerate convergence in deep and
|
|
physics-informed neural networks*. Journal of
|
|
Computational Physics 404 (2020): 109136.
|
|
DOI: `JCP 10.1016
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|
<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, gamma=None, fixed=None):
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super().__init__(alpha, beta, gamma, fixed)
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self._func = torch.sin
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class AdaptiveExp(AdaptiveActivationFunctionInterface):
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r"""
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Adaptive trainable :obj:`~torch.exp` function.
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Given the function :math:`\text{exp}:\mathbb{R}^n\rightarrow\mathbb{R}^n`,
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the adaptive function
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:math:`\text{exp}_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^n`
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is defined as:
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.. math::
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\text{exp}_{\text{adaptive}}({x}) = \alpha\,\text{exp}(\beta{x}),
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where :math:`\alpha,\,\beta` are trainable parameters.
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.. seealso::
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**Original reference**: Godfrey, Luke B., and Michael S. Gashler.
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*A continuum among logarithmic, linear, and exponential functions,
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and its potential to improve generalization in neural networks.*
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2015 7th international joint conference on knowledge discovery,
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knowledge engineering and knowledge management (IC3K).
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Vol. 1. IEEE, 2015. DOI: `arXiv preprint arXiv:1602.01321.
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<https://arxiv.org/abs/1602.01321>`_.
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Jagtap, Ameya D., Kenji Kawaguchi, and George Em Karniadakis. *Adaptive
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activation functions accelerate convergence in deep and
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physics-informed neural networks*. Journal of
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Computational Physics 404 (2020): 109136.
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DOI: `JCP 10.1016
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<https://doi.org/10.1016/j.jcp.2019.109136>`_.
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"""
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def __init__(self, alpha=None, beta=None, fixed=None):
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# only alpha, and beta parameters (gamma=0 fixed)
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if fixed is None:
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fixed = ["gamma"]
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else:
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check_consistency(fixed, str)
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fixed = list(fixed) + ["gamma"]
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# calling super
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super().__init__(alpha, beta, 0.0, fixed)
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self._func = torch.exp
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