Related papers: Accelerating Dynamical System Simulations with Con…
Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…
Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural…
Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the…
We introduce a neural network (NN) strictly governed by Newton's Law, with the nature required basis functions derived from the fundamental classic mechanics. Then, by classifying the training model as a quick procedure of 'force pattern'…
Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…
Continuous-time (CT) modeling has proven to provide improved sample efficiency and interpretability in learning the dynamical behavior of physical systems compared to discrete-time (DT) models. However, even with numerous recent…
Quasi-static time series (QSTS) simulations have great potential for evaluating the grid's ability to accommodate the large-scale integration of distributed energy resources. However, as grids expand and operate closer to their limits,…
Continuous-time neural processes are performant sequential decision-makers that are built by differential equations (DE). However, their expressive power when they are deployed on computers is bottlenecked by numerical DE solvers. This…
Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff…
We present a novel approach to accelerate iterative methods to solve nonlinear Schr\"odinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional…
A promising application of machine learning is the creation of low-cost surrogate models to mitigate computational bottlenecks in quantum many-body simulations. Here, we explore whether a neural network (NN) can be trained in the low-data…
Accurate thermal emission models of neutron stars are essential for constraining the dense matter equation of state. However, incorporating realistic magnetic field structures is computationally prohibitive, severely constraining feasible…
Neural networks (NNs) offer a path towards synthesizing and interpreting data on faster timescales than traditional physics-informed computational models. In this work we develop two neural networks relevant to equilibrium and shape control…
We study the applicability of a Deep Neural Network (DNN) approach to simulate one-dimensional non-relativistic fluid dynamics. Numerical fluid dynamical calculations are used to generate training data-sets corresponding to a broad range of…
Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way to accelerate simulations, but their practical deployment is…
We propose a novel neural preconditioned Newton (NP-Newton) method for solving parametric nonlinear systems of equations. To overcome the stagnation or instability of Newton iterations caused by unbalanced nonlinearities, we introduce a…
Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…