Related papers: AutoNumerics: An Autonomous, PDE-Agnostic Multi-Ag…
The escalating complexity of modern software imposes an unsustainable operational burden on Site Reliability Engineering (SRE) teams, demanding AI-driven automation that can emulate expert diagnostic reasoning. Existing solutions, from…
We design two classes of ultra-fast meta-solvers for linear systems arising after discretizing PDEs by combining neural operators with either simple iterative solvers, e.g., Jacobi and Gauss-Seidel, or with Krylov methods, e.g., GMRES and…
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…
Adapting production-level computer vision tools to bespoke scientific datasets is a critical "last mile" bottleneck. Current solutions are impractical: fine-tuning requires large annotated datasets scientists often lack, while manual code…
The deployment of autonomous agents for Computational Fluid Dynamics (CFD), is critically limited by the probabilistic nature of Large Language Models (LLMs), which struggle to enforce the strict conservation laws and numerical stability…
Fully automated self-driving laboratories are promising to enable high-throughput and large-scale scientific discovery by reducing repetitive labour. However, effective automation requires deep integration of laboratory knowledge, which is…
This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…
Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation…
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…
We introduce the Autoregressive PDE Emulator Benchmark (APEBench), a comprehensive benchmark suite to evaluate autoregressive neural emulators for solving partial differential equations. APEBench is based on JAX and provides a seamlessly…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Solving partial differential equations (PDEs) using neural methods has been a long-standing scientific and engineering research pursuit. Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to traditional…
The rapid advancement of large language models (LLMs) has driven the development of agentic systems capable of autonomously performing complex tasks. Despite their impressive capabilities, LLMs remain constrained by their internal knowledge…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…
Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…
We present new algorithms for a posteriori verification of neural networks (NNs) approximating solutions to PDEs. These verification algorithms compute accurate estimates of $L^p$ norms of NNs and their derivatives. When combined with…
Data preparation, which aims to transform heterogeneous and noisy raw tables into analysis-ready data, remains a major bottleneck in data science. Recent approaches leverage large language models (LLMs) to automate data preparation from…