Related papers: Automatic Differentiation using Operator Overloadi…
Machine learning models deployed in open-world scenarios often encounter unfamiliar conditions and perform poorly in unanticipated situations. As AI systems advance and find application in safety-critical domains, effectively handling…
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
Recent advances in computational materials science present novel opportunities for structure discovery and optimization, including uncovering of unsuspected compounds and metastable structures, electronic structure, surface, and…
We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multiscale hyperbolic heat system with quantum algorithms (hence…
The monodomain model is widely used in in-silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so…
This paper presents a method for modeling transient fluid flow in subsurface reservoir systems based on the developed neural operator architecture (TFNO-opt). Reservoir systems are complex dynamic objects with distributed parameters…
Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…
Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computation cost and storage resources because of the memory effect…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
We propose a variant of the $\theta$-scheme for diffuse interface models for two-phase flow, together with three new linearization techniques for the surface tension. These involve either additional stabilizing force terms, or a fully…
Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…
Stability is an important aspect of numerical methods for hyperbolic conservation laws and has received much interest. However, continuity in time is often assumed and only semidiscrete stability is studied. Thus, it is interesting to…
Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…
This paper investigates the temporal evolution of high-speed compressible fluids in irregular flow fields using the Fourier Neural Operator (FNO). We reconstruct the irregular flow field point set into sequential format compatible with FNO…
This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive…
Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on solving sequentially a set of related one-dimensional…