Publications related to Optimization Problem Coupled with Differential Equations: A Numerical Algorithm Mixing an Interior-Point Method and Event Detection

Related publications (38)

Combining physics-based and data-driven models: advancing the frontiers of research with scientific machine learning

Scientific Machine Learning (SciML) is a recently emerged research field which combines physics-based and data-driven models for the numerical approximation of differential problems. Physics-based models rely on the physical understanding of the problem at ...

2025

SPINN: Advancing Cosmological Simulations of Fuzzy Dark Matter with Physics Informed Neural Networks

Emma Elizabeth Tolley, Ashutosh Kumar Mishra

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving differential equations by integrating physical laws into the learning process. This work leverages PINNs to simulate gravitational collapse, a critical phenomenon in astro ...

2025

First and Zeroth-Order Implementations of the Regularized Newton Method with Lazy Approximated Hessians

Nikita Doikov

In this work, we develop first-order (Hessian-free) and zeroth-order (derivative-free) implementations of the Cubically Regularized Newton Method for solving general non-convex optimization problems. For that, we employ finite difference approximations of ...

SPRINGER/PLENUM PUBLISHERS2025

Dimensionless Group-Driven Ensemble Neural Networks for Robust Design Optimisation in Engineering

Jürg Alexander Schiffmann, Soheyl Massoudi

This work aims to develop a scalable surrogate modelling framework for robust multidisciplinary design optimisation (RMDO) in complex engineering systems. Focusing on gas-bearing supported rotors, it addresses the need to maintain system performance under ...

Oxford University Press (OUP)2025

Integer Linear Programming for Unsupervised Training Set Selection in Molecular Machine Learning

Anne-Clémence Corminboeuf, Friedrich Eisenbrand, Rubén Laplaza Solanas, Puck Elisabeth van Gerwen, Ksenia Briling, Jan Weinreich, Matthieu Nicolas Haeberle

Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning (ML) applied to chemistry, we demonstrate the relev ...

IOP Publishing Ltd2025

A shortcut model for batch distillation columns using pertinent effective factors

Dominique Bonvin

A shortcut model is a low-order model that provides a simplified representation of a complex process, thereby enabling faster and more efficient analysis, design and optimization without the computational intensity of a full-scale model. For continuous dis ...

Elsevier2025

Convex Computation of Value-at-risk Bounds for Stochastic Processes

Matteo Raphael Tacchi

This article formulates algorithms to upper-bound the maximum value-at-risk (VaR) of a state function along trajectories of stochastic processes. The VaR is upper bounded by two methods: minimax tail-bounds (Cantelli/Vysochanskij-Petunin) and Expected Shor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2025

A Stochastic Approach to Contact-rich Manipulation

Julius Maximilian Jankowski

For robots to operate in unstructured environments, they are required to interact with objects through contact. Those contacts may be used to push objects to the side, deform objects, or manipulate objects in-hand. This thesis addresses the problem of cont ...

EPFL2025

Ambipolar diffusion and the mass-to-flux ratio in a turbulent collapsing cloud

Aris Evangelos Tritsis

Context. The formation of stars is governed by the intricate interplay of nonideal magnetohydrodynamic (MHD) effects, gravity, and turbulence. Computational challenges have hindered a comprehensive 3D exploration of this interplay, posing a longstanding ch ...

2025

Residual-based attention in physics-informed neural networks

Nikolaos Stergiopoulos, Sokratis Anagnostopoulos

Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...

Elsevier Science Sa2024

From low-rank retractions to dynamical low-rank approximation and back

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Springer2024

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Maude Girardin, Marco Picasso, Alexandre Caboussat

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

Elsevier Science Sa2024

Scalable constrained optimization

Maria-Luiza Vladarean

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

EPFL2024

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Nature Portfolio2024

High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

Roya Moghaddasi Fereidani

Molecular quantum dynamics simulations are essential for understanding many fundamental phenomena in physics and chemistry. They often require solving the time-dependent Schrödinger equation for molecular nuclei, which is challenging even for medium-sized ...

EPFL2024

The effect of smooth parametrizations on nonconvex optimization landscapes

Nicolas Boumal

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

Springer Heidelberg2024

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

Fabio Nobile, Tommaso Vanzan

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

2024

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Siam Publications2024

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Jan Sickmann Hesthaven, Niccolo' Discacciati

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

Elsevier Science Sa2024

A Reduced Order Model for Domain Decompositions with Non-conforming Interfaces

Alfio Quarteroni, Andrea Manzoni

In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems wi ...

Springer/Plenum Publishers2024