Related papers: Hebbian Physics Networks: A Self-Organizing Comput…

Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of random tensor networks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond…

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…

In this work, we are interested in tree-shaped networks of freely vibrating beams which are geometrically exact (GEB) -- in the sense that large motions (deflections, rotations) are accounted for in addition to shearing -- and linked by…

Backpropagation (BP) has been pivotal in advancing machine learning and remains essential in computational applications and comparative studies of biological and artificial neural networks. Despite its widespread use, the implementation of…

The recently introduced Thermodynamic Binding Networks (TBN) model was developed with the purpose of studying self-assembling systems by focusing on their thermodynamically favorable final states, and ignoring the kinetic pathways through…

The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We…

Through periodic Training we can gradually buildup a reproducible responses in a disordered system where plasticity dominates over elasticity as is known in classical amorphous materials and soft matter 1, 6. Here we show that a similar…

Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum…

The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear…

We investigate associative-memory behavior in a reconfigurable particle packing programmed by purely local cyclic driving. The system is a two-dimensional bidisperse Lennard--Jones particle assembly with periodic boundaries evolved under…

Real-time, physically-consistent predictions on low-power edge devices is critical for the next generation embodied AI systems, yet it remains a major challenge. Physics-Informed Neural Networks (PINNs) combine data-driven learning with…

Physical networks are made of nodes and links that are physical objects embedded in a geometric space. Understanding how the mutual volume exclusion between these elements affects the structure and function of physical networks calls for a…

We show that deep networks can be trained using Hebbian updates yielding similar performance to ordinary back-propagation on challenging image datasets. To overcome the unrealistic symmetry in connections between layers, implicit in…

Tensegrity structures possess intrinsic geometric symmetries that govern their dynamic behavior. However, most existing physics-informed neural network (PINN) approaches for tensegrity dynamics do not explicitly exploit these symmetries,…

In turbulence modeling, we are concerned with finding closure models that represent the effect of the subgrid scales on the resolved scales. Recent approaches gravitate towards machine learning techniques to construct such models. However,…

We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides…

Topology optimization is used for the design of high-performance structures but remains fundamentally limited by its iterative nature, requiring repeated finite element analyses that prevent real-time deployment and large-scale design…

As a network-based functional approximator, we have proposed a "Lagrangian Density Space-Time Deep Neural Networks" (LDDNN) topology. It is qualified for unsupervised training and learning to predict the dynamics of underlying physical…

Data-driven algorithms, in particular neural networks, can emulate the effect of sub-grid scale processes in coarse-resolution climate models if trained on high-resolution climate simulations. However, they may violate key physical…

Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities such as matter, energy and charge flow from outer reservoirs across a system, and how they irreversibly degrade from one form to another. Stochastic…