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Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves. However, current accuracy-based evaluations do not fully consider two central…

Automated Machine Learning (AutoML) is the problem of automatically finding the pipeline with the best generalization performance on some given dataset. AutoML has received enormous attention in the last decade and has been addressed with…

We present a general and scalable framework for the automated discovery of optimal meta-solvers for the solution of time-dependent nonlinear partial differential equations after appropriate discretization. By integrating classical numerical…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

Self-driving laboratories (SDLs) close the loop between experiment design, automated execution, and data-driven decision making, and they provide a demanding testbed for agentic AI under expensive actions, noisy and delayed feedback, strict…

Agentic systems are becoming more capable: agents define strategies, take actions, and interact with different environments. This autonomy poses serious challenges for overseeing and assessing agent behavior. Most current tools are limited,…

Large language models (LLMs) serve as an active and promising field of generative artificial intelligence and have demonstrated abilities to perform complex tasks in multiple domains, including mathematical and scientific reasoning. In this…

The integration of Large Language Models (LLMs) into software engineering has driven a transition from traditional rule-based systems to autonomous agentic systems capable of solving complex problems. However, systematic progress is…

We introduce DDE-Solver, a Maple package designed for solving Discrete Differential Equations (DDEs). These equations are functional equations relating algebraically a formal power series F(t, u) with polynomial coefficients in a…

Recent advances in deep-learning based denoising methods have improved Low-Dose CT image quality. However, due to distinct HU distributions and diverse anatomical characteristics, a single model often struggles to generalize across multiple…

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…

Existing unstructured data analytics systems rely on experts to write code and manage complex analysis workflows, making them both expensive and time-consuming. To address these challenges, we introduce AgenticData, an innovative agentic…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

We introduce the AutoGRAMS framework for programming multi-step interactions with language models. AutoGRAMS represents AI agents as a graph, where each node can execute either a language modeling instruction or traditional code. Likewise,…

Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…

This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential…

Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed…

Numerical simulations for engineering applications solve partial differential equations (PDE) to model various physical processes. Traditional PDE solvers are very accurate but computationally costly. On the other hand, Machine Learning…