Local learning for stable backpropagation-free neural network training towards physical learning

While backpropagation and automatic differentiation have driven deep learning's success, the physical limits of chip manufacturing and rising environmental costs of deep learning motivate alternative learning paradigms such as physical neural networks. However, most existing physical neural networks still rely on digital computing for training, largely because backpropagation and automatic differentiation are difficult to realize in physical systems. We introduce FFzero, a forward-only learning framework enabling stable neural network training without backpropagation or automatic differentiation. FFzero combines layer-wise local learning, prototype-based representations, and directional-derivative-based optimization through forward evaluations only. We show that local learning is effective under forward-only optimization, where backpropagation fails. FFzero generalizes to multilayer perceptron and convolutional neural networks across classification and regression. Using a simulated photonic neural network as an example, we demonstrate that FFzero provides a viable path toward backpropagation-free in-situ physical learning.

Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)

Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these trade-offs, we present Input-Convex Kolmogorov-Arnold Networks (ICKANs) for learning polyconvex hyperelastic constitutive laws. ICKANs leverage the Kolmogorov-Arnold representation, decomposing the model into compositions of trainable univariate spline-based activation functions for rich expressivity. We introduce trainable input-convex splines within the KAN architecture, ensuring physically admissible polyconvex hyperelastic models. The resulting models are both compact and interpretable, enabling explicit extraction of analytical constitutive relationships through an input-convex symbolic regression techinque. Through unsupervised training on full-field strain data and limited global force measurements, ICKANs accurately capture nonlinear stress-strain behavior across diverse strain states. Finite element simulations of unseen geometries with trained ICKAN hyperelastic constitutive models confirm the framework's robustness and generalization capability.