Adaptive Functions (#272)

* adaptive function improvement

---------

Co-authored-by: Dario Coscia <dariocoscia@Dario-Coscia.local>

pina/model/layers/__init__.py

@@ -11,6 +11,7 @@ __all__ = [
     "PODBlock",
     "PeriodicBoundaryEmbedding",
     "AVNOBlock",
+    "AdaptiveActivationFunction"
 ]
 
 from .convolution_2d import ContinuousConvBlock
@@ -24,3 +25,4 @@ from .fourier import FourierBlock1D, FourierBlock2D, FourierBlock3D
 from .pod import PODBlock
 from .embedding import PeriodicBoundaryEmbedding
 from .avno_layer import AVNOBlock
+from .adaptive_func import AdaptiveActivationFunction

pina/model/layers/adaptive_func.py

@@ -0,0 +1,151 @@
+""" Module for adaptive functions. """
+
+import torch
+from pina.utils import check_consistency
+
+
+class AdaptiveActivationFunction(torch.nn.Module):
+    r"""
+    The :class:`~pina.model.layers.adaptive_func.AdaptiveActivationFunction`
+    class makes a :class:`torch.nn.Module` activation function into an adaptive
+    trainable activation function.
+
+    Given a function :math:`f:\mathbb{R}^n\rightarrow\mathbb{R}^m`, the adaptive
+    function :math:`f_{\text{adaptive}}:\mathbb{R}^n\rightarrow\mathbb{R}^m`
+    is defined as:
+
+    .. math::
+        f_{\text{adaptive}}(\mathbf{x}) = \alpha\,f(\beta\mathbf{x}+\gamma),
+
+    where :math:`\alpha,\,\beta,\,\gamma` are trainable parameters.
+
+    :Example:
+        >>> import torch
+        >>> from pina.model.layers import AdaptiveActivationFunction
+        >>>
+        >>> # simple adaptive function with all trainable parameters
+        >>> AdaptiveTanh = AdaptiveActivationFunction(torch.nn.Tanh())
+        >>> AdaptiveTanh(torch.rand(3))
+        tensor([0.1084, 0.3931, 0.7294], grad_fn=<MulBackward0>)
+        >>> AdaptiveTanh.alpha
+        Parameter containing:
+        tensor(1., requires_grad=True)
+        >>>
+        >>> # simple adaptive function with trainable parameters fixed alpha
+        >>> AdaptiveTanh = AdaptiveActivationFunction(torch.nn.Tanh(),
+        ...                                           fixed=['alpha'])
+        >>> AdaptiveTanh.alpha
+        tensor(1.)
+        >>> AdaptiveTanh.beta
+        Parameter containing:
+        tensor(1., requires_grad=True)
+        >>>
+    
+    .. seealso::
+
+        **Original reference**: Godfrey, Luke B., and Michael S. Gashler.
+        *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>`_.
+    
+    """
+
+    def __init__(self, func, alpha=None, beta=None, gamma=None, fixed=None):
+        """
+        Initializes the AdaptiveActivationFunction module.
+
+        :param callable func: The original collable function. It could be an
+            initialized :meth:`torch.nn.Module`, or a python callable function.
+        :param float | complex alpha: Scaling parameter alpha.
+            Defaults to ``None``. When ``None`` is passed,
+            the variable is initialized to 1.
+        :param float | complex beta: Scaling parameter beta.
+            Defaults to ``None``. When ``None`` is passed,
+            the variable is initialized to 1.
+        :param float | complex gamma: Shifting parameter gamma.
+            Defaults to ``None``. When ``None`` is passed,
+            the variable is initialized to 1.
+        :param list fixed: List of parameters to fix during training,
+            i.e. not optimized (``requires_grad`` set to ``False``).
+            Options are ['alpha', 'beta', 'gamma']. Defaults to None.
+        """
+        super().__init__()
+
+        # see if there are fixed variables
+        if fixed is not None:
+            check_consistency(fixed, str)
+            if not all(key in ['alpha', 'beta', 'gamma'] for key in fixed):
+                raise TypeError("Fixed keys must be in "
+                                "['alpha', 'beta', 'gamma'].")
+
+        # initialize alpha, beta, gamma if they are None
+        if alpha is None:
+            alpha = 1.
+        if beta is None:
+            beta = 1.
+        if gamma is None:
+            gamma = 0.
+
+        # checking consistency
+        check_consistency(alpha, (float, complex))
+        check_consistency(beta, (float, complex))
+        check_consistency(gamma, (float, complex))
+        if not callable(func):
+            raise ValueError("Function must be a callable function.")
+
+        # registering as tensors
+        alpha = torch.tensor(alpha, requires_grad=False)
+        beta = torch.tensor(beta, requires_grad=False)
+        gamma = torch.tensor(gamma, requires_grad=False)
+
+        # setting not fixed variables as torch.nn.Parameter with gradient
+        # registering the buffer for the one which are fixed, buffers by
+        # default are saved alongside trainable parameters
+        if 'alpha' not in (fixed or []):
+            self._alpha = torch.nn.Parameter(alpha, requires_grad=True)
+        else:
+            self.register_buffer('alpha', alpha)
+            
+        if 'beta' not in (fixed or []):
+            self._beta = torch.nn.Parameter(beta, requires_grad=True)
+        else:
+            self.register_buffer('beta', beta)
+            
+        if 'gamma' not in (fixed or []):
+            self._gamma = torch.nn.Parameter(gamma, requires_grad=True)
+        else:
+            self.register_buffer('gamma', gamma)
+
+        # registering function
+        self._func = func
+
+    def forward(self, x):
+        """
+        Forward pass of the function.
+        Applies the function to the input elementwise.
+        """
+        return self.alpha * (self._func(self.beta * x + self.gamma))
+    
+    @property
+    def alpha(self):
+        """
+        The alpha variable
+        """
+        return self._alpha
+    
+    @property
+    def beta(self):
+        """
+        The alpha variable
+        """
+        return self._beta
+    
+    @property
+    def gamma(self):
+        """
+        The alpha variable
+        """
+        return self._gamma