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We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level. Each task pairs a natural-language problem with a Lean~4 formal statement, and…
A large number of computational scientific research projects make use of open source software packages. However, the development process of such tools frequently differs from conventional software development; partly because of the nature…
Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and…
Application Programming Interfaces (APIs), which encapsulate the implementation of specific functions as interfaces, greatly improve the efficiency of modern software development. As numbers of APIs spring up nowadays, developers can hardly…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…
There is a growing need for Large Language Models (LLMs) to effectively use tools and external Application Programming Interfaces (APIs) to plan and complete tasks. As such, there is tremendous interest in methods that can acquire…
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…
Software development is getting changed so rapidly. It will be highly benefited if we can accelerate software development process by guiding developers. Appropriate guidelines and accurate recommendations to developers during development…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
No single Automatic Differentiation (AD) system is the optimal choice for all problems. This means informed selection of an AD system and combinations can be a problem-specific variable that can greatly impact performance. In the Julia…
Important computational physics problems are often large-scale in nature, and it is highly desirable to have robust and high performing computational frameworks that can quickly address these problems. However, it is no trivial task to…
The rapid rise of scientific machine learning (SciML) has expanded the role of differentiable modeling, surrogate modeling, and data-driven constitutive laws in large-scale simulation. The JAX framework provides an attractive environment…
In this paper, we discuss the need for an integrated software stack that unites artificial intelligence (AI) and modeling and simulation (ModSim) tools to advance scientific discovery. The authors advocate for a unified AI/ModSim software…
Scientific computing is an essential tool for scientific discovery and engineering design, and its computational cost is always a main concern in practice. To accelerate scientific computing, it is a promising approach to use machine…
Continuous dynamical systems, characterized by differential equations, are ubiquitously used to model several important problems: plasma dynamics, flow through porous media, weather forecasting, and epidemic dynamics. Recently, a wide range…
The breakthrough in Deep Learning neural networks has transformed the use of AI and machine learning technologies for the analysis of very large experimental datasets. These datasets are typically generated by large-scale experimental…
Machine Learning (ML) and Deep Learning (DL) innovations are being introduced at such a rapid pace that researchers are hard-pressed to analyze and study them. The complicated procedures for evaluating innovations, along with the lack of…
We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…
Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a…