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Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and…

In graph representation learning, it is important that the complex geometric structure of the input graph, e.g. hidden relations among nodes, is well captured in embedding space. However, standard Euclidean embedding spaces have a limited…

Wireless physical neural networks (WPNNs) have emerged as a promising paradigm for performing neural computation directly in the physical layer of wireless systems, offering low latency and high energy efficiency. However, most existing…

Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear…

Expressivity plays a fundamental role in evaluating deep neural networks, and it is closely related to understanding the limit of performance improvement. In this paper, we propose a three-pipeline training framework based on critical…

The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While nonlinear computations can be implemented successfully in spiking neural networks, this…

With the versatile manipulation capability, programmable metasurfaces are rapidly advancing in their intelligence, integration, and commercialization levels. However, as the programmable metasurfaces scale up, their control configuration…

The functional and structural representation of the brain as a complex network is marked by the fact that the comparison of noisy and intrinsically correlated high-dimensional structures between experimental conditions or groups shuns…

Accurate prediction of permeability in porous media is essential for modeling subsurface flow. While pure data-driven models offer computational efficiency, they often lack generalization across scales and do not incorporate explicit…

The ability of mechanical systems to perform basic computations has gained traction over recent years, providing an unconventional alternative to digital computing in off grid, low power, and severe environments which render the majority of…

Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…

In recent years, metasurfaces composed of lumped circuit components, including nonlinear Schottky diodes, have been reported to be capable of sensing particular electromagnetic waves even at the same frequency depending on their waveforms,…

Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights. Recent work has improved the training stability of…

In this paper, a method based on the physics-informed neural networks (PINNs) is presented to model in-plane crack problems in the linear elastic fracture mechanics. Instead of forming a mesh, the PINNs is meshless and can be trained on…

This paper investigates propagation of SH-waves in a layered composite structure consisting of a pre-stressed functionally graded magnetoelastic orthotropic layer overlying a pre-stressed functionally graded orthotropic half-space under the…

We study deep neural networks with polynomial activations, particularly their expressive power. For a fixed architecture and activation degree, a polynomial neural network defines an algebraic map from weights to polynomials. The image of…

Polynomial Neural Networks (PNNs) possess a rich algebraic and geometric structure. However, their identifiability -- a key property for ensuring interpretability -- remains poorly understood. In this work, we present a comprehensive…

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…

This work presents a physics-driven machine learning framework for the simulation of acoustic scattering problems. The proposed framework relies on a physics-informed neural network (PINN) architecture that leverages prior knowledge based…

The human brain displays rich communication dynamics that are thought to be particularly well-reflected in its marked community structure. Yet, the precise relationship between community structure in structural brain networks and the…