Related papers: A Kolmogorov-Arnold Surrogate Model for Chemical E…

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

Robust and efficient solvers for coupled-adjoint linear systems are crucial to successful aerostructural optimization. Monolithic and partitioned strategies can be applied. The monolithic approach is expected to offer better robustness and…

Neural network surrogate models have emerged as a promising approach to model solution fields for a wide variety of boundary value problems encountered in physical modeling. Stochastic problems represent an area of particularly high…

Deep learning models have revolutionized various domains, with Multi-Layer Perceptrons (MLPs) being a cornerstone for tasks like data regression and image classification. However, a recent study has introduced Kolmogorov-Arnold Networks…

Optimizing the locations of multiple CO2 injection wells will be essential as we proceed from demonstration-scale to large-scale carbon storage operations. Well placement optimization is, however, a computationally intensive task because…

Surrogate modeling is a powerful methodology in chemical process engineering, frequently employed to accelerate optimization tasks where traditional flowsheet simulators are computationally prohibitive. However, the state-of-the-art is…

Data science has emerged as fourth paradigm of scientific exploration. However many machine learning models operate as black boxes offering limited insight into the reasoning behind their predictions. This lack of transparency is one of the…

The Kolmogorov-Arnold representation theorem states that any continuous multivariable function can be exactly represented as a finite superposition of continuous single variable functions. Subsequent simplifications of this representation…

Surrogate models of numerical relativity simulations of merging black holes provide the most accurate tools for gravitational-wave data analysis. Neural network-based surrogates promise evaluation speedups, but their accuracy relies on…

The design of new High Entropy Alloys that can achieve exceptional mechanical properties is presently of great interest to the materials science community. However, due to the difficulty of designing these alloys using traditional methods,…

We present a data-driven, space-time continuous framework to learn surrogate models for complex physical systems described by advection-dominated partial differential equations. Those systems have slow-decaying Kolmogorov n-width that…

This paper describes novel algorithms for the identification of (almost-)resonant behavior in scattering problems. Our methods, relying on rational approximation, aim at building surrogate models of what we call "field amplification",…

The increasing use of stochastic models for describing complex phenomena warrants surrogate models that capture the reference model characteristics at a fraction of the computational cost, foregoing potentially expensive Monte Carlo…

Modelling rock-fluid interaction requires solving a set of partial differential equations (PDEs) to predict the flow behaviour and the reactions of the fluid with the rock on the interfaces. Conventional high-fidelity numerical models…

By utilising their adaptive activation functions, Kolmogorov-Arnold Networks (KANs) can be applied in a novel way for the diverse machine learning tasks, including cyber threat detection. KANs substitute conventional linear weights with…

Reliable plasma transport modeling for magnetic confinement fusion depends on accurately resolving the ion charge state distribution and radiative power losses of the plasma. These quantities can be obtained from solutions of a…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Kolmogorov-Arnold Networks (KANs) shift neural computation from linear layers to learnable nonlinear edge functions, but implementing these nonlinearities efficiently in hardware remains an open challenge. Here we introduce a physical…

High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…

A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures,…