Related papers: Physics-based linear regression for high-dimension…
This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy…
The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high-dimensional inputs/outputs (I/O), conventional approaches usually use a low-dimensional manifold to…
Simulation models are widely used in practice to facilitate decision-making in a complex, dynamic and stochastic environment. But they are computationally expensive to execute and optimize, due to lack of analytical tractability. Simulation…
Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…
The prohibitive cost of performing Uncertainty Quantification (UQ) tasks with a very large number of input parameters can be addressed, if the response exhibits some special structure that can be discovered and exploited. Several physical…
This work proposes a data-driven surrogate modeling framework for cost-effectively inferring the torque of a permanent magnet synchronous machine under geometric design variations. The framework is separated into a reduced-order modeling…
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
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…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…
Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…
Machine learning models play a vital role in time series forecasting. These models, however, often overlook an important element: point uncertainty estimates. Incorporating these estimates is crucial for effective risk management, informed…
Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…
Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…
Inverse modeling for computing a high-dimensional spatially-varying property field from indirect sparse and noisy observations is a challenging problem. This is due to the complex physical system of interest often expressed in the form of…
Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space…
Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…
This work introduces a novel methodology to derive physical scalings for input features from data. The approach developed in this article relies on the maximization of mutual information to derive optimal nonlinear combinations of input…