Related papers: A conservative hybrid physics-informed neural netw…
We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP)…
Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online…
We propose a Kolmogorov-Arnold Representation-based Hamiltonian Neural Network (KAR-HNN) that replaces the Multilayer Perceptrons (MLPs) with univariate transformations. While Hamiltonian Neural Networks (HNNs) ensure energy conservation by…
In this study, we derive Probably Approximately Correct (PAC) bounds on the asymptotic sample-complexity for RL within the infinite-horizon Markov Decision Process (MDP) setting that are sharper than those in existing literature. The…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
We derive the discretized Maxwell's equations using the discrete variational derivative method (DVDM), calculate the evolution equation of the constraint, and confirm that the equation is satisfied at the discrete level. Numerical…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
We present a novel class of high-order space-time finite element schemes for the Poisson-Nernst-Planck (PNP) equations. We prove that our schemes are mass conservative, positivity preserving, and unconditionally energy stable for any order…
A fundamental objective of materials modeling is identifying atomic structures that align with experimental observables. Conventional approaches for disordered materials involve sampling from thermodynamic ensembles and hoping for an…
For an infinite-horizon control problem, the optimal control can be represented by the stable manifold of the characteristic Hamiltonian system of Hamilton-Jacobi-Bellman (HJB) equation in a semiglobal domain. In this paper, we first…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We propose Weak and Entropy PINNs (WE-PINNs) for the approximation of entropy solutions to nonlinear hyperbolic conservation laws. Standard physics-informed neural networks enforce governing equations in strong differential form, an…
Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…
In this paper, we propose the Adaptive Physics-Informed Neural Networks (APINNs) for accurate and efficient simulation-free Bayesian parameter estimation via Markov-Chain Monte Carlo (MCMC). We specifically focus on a class of parameter…
There are several numerical models that describe real phenomena being used to solve complex problems. For example, an accurate numerical breast model can provide assistance to surgeons with visual information of the breast as a result of a…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…
Data sparsity is a common issue to train machine learning tools such as neural networks for engineering and scientific applications, where experiments and simulations are expensive. Recently physics-constrained neural networks (PCNNs) were…
We present a physics-constrained neural network (PCNN) approach to solving Maxwell's equations for the electromagnetic fields of intense relativistic charged particle beams. We create a 3D convolutional PCNN to map time-varying current and…
In this paper we present a convex formulation of the Model Predictive Control (MPC) optimisation for energy management in hybrid electric vehicles, and an Alternating Direction Method of Multipliers (ADMM) algorithm for its solution. We…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…