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Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
Physics-Informed Neural Networks (PINNs) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard…
This paper presents a novel method for utilizing fine-tuned Large Language Models (LLMs) to minimize data requirements in load profile analysis, demonstrated through the restoration of missing data in power system load profiles. A two-stage…
In several industrial applications, such as crystallization, pollution control, and flow assurance, an accurate understanding of the aqueous electrolyte solutions is crucial. Electrolyte equilibrium calculation contributes with the design…
PySEMTools is a Python-based library for post-processing simulation data produced with high-order hexahedral elements in the context of the spectral element method in computational fluid dynamics. It aims to minimize intermediate steps…
Large Language Models (LLMs) have significantly advanced artificial intelligence by optimizing traditional Natural Language Processing (NLP) workflows, facilitating their integration into various systems. Many such NLP systems, including…
Optimization on manifolds is a class of methods for optimization of an objective function, subject to constraints which are smooth, in the sense that the set of points which satisfy the constraints admits the structure of a differentiable…
In this paper, we propose a linearized finite element method (FEM) for solving the cubic nonlinear Schr\"{o}dinger equation with wave operator. In this method, a modified leap-frog scheme is applied for time discretization and a Galerkin…
Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which…
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…
Linear Mixed-Effects (LME) models are a fundamental tool for modeling clustered data, including cohort studies, longitudinal data analysis, and meta-analysis. The design and analysis of variable selection methods for LMEs is considerably…
The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic PDE that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
The Active Matter Evaluation Package (AMEP) is a Python library for analyzing simulation data of particle-based and continuum simulations. It provides a powerful and simple interface for handling large data sets and for calculating and…
Nonlinear filter has long been an important problem in practical industrial applications. The Yau-Yau method is a highly versatile framework that transforms nonlinear filtering problems into initial-value problems governed by the Forward…
In this work, we present our generic framework to construct, simulate, and calibrate dynamical systems in Python 3. Its goal is to reduce the time it takes to implement a dynamical system with $n$-dimensional states represented by coupled…
Language models (LMs) have demonstrated remarkable capabilities in NLP, yet adapting them efficiently and robustly to specific tasks remains challenging. As their scale and complexity grow, fine-tuning LMs on labelled data often…
We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time points. The algorithm is obtained through a delicate…
An automated framework is presented for the numerical solution of optimal control problems with PDEs as constraints, in both the stationary and instationary settings. The associated code can solve both linear and non-linear problems, and…
In this work, we explore advanced machine learning techniques for minimizing Gibbs free energy in full 3D micromagnetic simulations. Building on Brown's bounds for magnetostatic self-energy, we revisit their application in the context of…