Related papers: A multi-physics compiler for generating numerical …
In perturbative calculations, e.g., in the setting of Quantum Chromodynamics (QCD) one aims at the evaluation of Feynman integrals. Here one is often faced with the problem to simplify multiple nested integrals or sums to expressions in…
Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations…
Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…
A low-dissipative solution framework integrating various types of high-order time scheme is proposed and implemented based on the open-source C++ library OpenFOAM. This framework aims to introduce different categories of low-dissipative…
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical methods to solve fluid flows. The finite volume method (FVM) is an important one. In FVM, space is discretized to many grid cells. When the number of grid…
Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been…
Quantum computers promise to solve several categories of problems faster than classical computers ever could. Current research mostly focuses on qubits, i.e., systems where the unit of information can assume only two levels. However, the…
This paper treats comprehensively the construction of problems from nonlinear dynamics and constrained optimization amenable to parameter continuation techniques and with particular emphasis on multi-segment boundary-value problems with…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
The increasing complexity and scale of photonic and electromagnetic devices demand efficient and accurate numerical solvers. In this work, we develop a parallel overlapping domain decomposition method (DDM) based on the finite-difference…
Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus Project is a flexible, open-source, parallelized computational framework for solving general partial differential equations using…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
Real-world optimization problems are often constrained by complex physical laws that limit computational scalability. These constraints are inherently tied to complex regions, and thus learning models that incorporate physical and geometric…
Interest in applying Artificial Intelligence (AI) techniques to compiler optimizations is increasing rapidly, but compiler research has a high entry barrier. Unlike in other domains, compiler and AI researchers do not have access to the…
Modeling hydrological fracture networks is a hallmark challenge in computational earth sciences. Accurately predicting critical features of fracture systems, e.g. percolation, can require solving large linear systems far beyond current or…
Constructing fast samplers for unconditional diffusion and flow-matching models has received much attention recently; however, existing methods for solving inverse problems, such as super-resolution, inpainting, or deblurring, still require…
Computational Fluid Dynamics (CFD) is an essential simulation tool in engineering, yet its steep learning curve and complex manual setup create significant barriers. To address these challenges, we introduce Foam-Agent, a multi-agent…
In this paper, we present a methodology to achieve high-fidelity simulations of chemically reacting hypersonic flows and demonstrate our numerical solver's capabilities on a selection of configurations. The numerical tools are developed…
Simulating flow problems is at the core of many engineering applications but often requires high computational effort, especially when dealing with complex models. This work presents a novel approach for resolving flow problems using the…
Generating large-scale, physically consistent AC Optimal Power Flow (ACOPF) datasets is essential for modern data-driven power system applications. The central challenge lies in balancing solution accuracy with computational efficiency.…