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Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

In the context of model-driven development, ensuring the correctness and consistency of evolving models is paramount. This paper investigates the application of Dynamic Symbolic Execution (DSE) for semantic difference analysis of…

Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…

In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…

Many models of physical systems, such as mechanical and electrical networks, exhibit algebraic constraints that arise from subsystem interconnections and underlying physical laws. Such systems are commonly formulated as…

Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…

As the number of deep learning frameworks increase and certain ones gain popularity, it spurs the discussion of what methodologies are employed by these frameworks and the reasoning behind them. The goal of this survey is to study how…

We propose a framework for training neural networks that are coupled with partial differential equations (PDEs) in a parallel computing environment. Unlike most distributed computing frameworks for deep neural networks, our focus is to…

A challenge for renewable and hybrid power systems is the dynamically stable integration of Renewable Energy Sources (RES). This paper specifically investigates the influence of intermittent RES and measurement delays from power electronic…

Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…

Differential-algebraic equations (DAEs) are widely used for modeling of dynamical systems. In numerical analysis of DAEs, consistent initialization and index reduction are important preprocessing prior to numerical integration. Existing DAE…

While frontier formal mathematics systems now routinely develop repository-scale proof engineering artifacts requiring multi-file coordination and semantic correctness beyond compilation, existing evaluation benchmarks remain focused on…

The conventional evaluation protocols on machine learning models rely heavily on a labeled, i.i.d-assumed testing dataset, which is not often present in real world applications. The Automated Model Evaluation (AutoEval) shows an alternative…

ALHEP is the symbolic algebra program for high-energy physics. It deals with amplitudes calculation, matrix element squaring, Wick theorem, dimensional regularization, tensor reduction of loop integrals and simplification of final…

Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. Deep-learning methods, however, find very challenging learning stiff dynamics. In this paper, we develop DAE-PINN, the…

The Fast Multipole Method (FMM) computes pairwise interactions between particles with an efficiency that scales linearly with the number of particles. The method works by grouping particles based on their spatial distribution and…

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non immersed fractures. The so called…

In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we…

The ``black-box'' nature of deep learning models presents a significant barrier to their adoption for scientific discovery, where interpretability is paramount. This challenge is especially pronounced in discovering the governing equations…

Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify…