Related papers: Multiscale Neural Operator: Learning Fast and Grid…

Specifying a governing physical model in the presence of missing physics and recovering its parameters are two intertwined and fundamental problems in science. Modern machine learning allows one to circumvent these, via emulators and…

The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the…

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this…

Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and…

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be…

This article builds on the recently proposed RB-ML-ROM approach for parameterized parabolic PDEs and proposes a novel hierarchical Trust Region algorithm for solving parabolic PDE constrained optimization problems. Instead of using a…

We consider the problem of constructing surrogate operators for parameter-to-solution maps arising from parametric partial differential equations, where repeated forward model evaluations are computationally expensive. We present a…

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many…

Understanding structure-property relations is essential to optimally design materials for specific applications. Two-scale simulations are often employed to analyze the effect of the microstructure on a component's macroscopic properties.…

In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

Hyperparameter optimization is the process of identifying the appropriate hyperparameter configuration of a given machine learning model with regard to a given learning task. For smaller data sets, an exhaustive search is possible; However,…

Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose…

Biophysical neural system simulations are among the most computationally demanding scientific applications, and their optimization requires navigating high-dimensional parameter spaces under numerous constraints that impose a binary…

Decision support systems often rely on solving complex optimization problems that may require to estimate uncertain parameters beforehand. Recent studies have shown how using traditionally trained estimators for this task can lead to…

We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The method aims at reducing…

We present a scalable framework for learning deterministic and probabilistic neural surrogates for high-resolution 3D physics simulations. We introduce a hybrid CNN-Transformer backbone architecture targeted for 3D physics simulations,…

A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…

Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we…

The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making…

It is not uncommon that meta-heuristic algorithms contain some intrinsic parameters, the optimal configuration of which is crucial for achieving their peak performance. However, evaluating the effectiveness of a configuration is expensive,…