Related papers: Physics-constrained Gaussian Processes for Predict…
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…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
We propose a modeling framework for stochastic systems, termed Gaussian behaviors, that describes finite-length trajectories of a system as a Gaussian process. The proposed model naturally quantifies the uncertainty in the trajectories, yet…
We present a new method for real-time physics-based simulation supporting many different types of hyperelastic materials. Previous methods such as Position Based or Projective Dynamics are fast, but support only limited selection of…
We set forth a new method for generating model-agnostic, nonparametric priors for neutron star equation-of-state inference that are stable, causal and thermodynamically consistent by construction. This generalizes Gaussian processes to…
This paper presents a probabilistic surrogate model for the accelerated design of electric vehicle battery enclosures with a focus on crash performance. The study integrates high-throughput finite element simulations and Gaussian Process…
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…
Many numerical algorithms have been established to reconstruct pressure fields from measured kinematic data with noise by Particle Image Velocimetry (PIV), such as the Pressure Poisson solver and the Omni-Directional Integration (ODI)…
A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given appropriate datasets, the model can be used to regress the analytical value of the…
Solutions of first-order nonlinear hyperbolic conservation laws typically develop shocks in finite time even with smooth initial conditions. However, in heterogeneous media with rapid spatial variation, shock formation may be delayed or…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
By using the Hugoniot curve in detonics as a Riemann invariant of a velocity-pressure model, we get a conservative hyperbolic system similar to the Euler equations. The only differences are the larger value of the adiabatic constant (=…
Gaussian states, operations, and measurements are central building blocks for continuous-variable quantum information processing which paves the way for abundant applications, especially including network-based quantum computation and…
In this article, we present a description of the behaviour of shock-compressed solid materials following the Geometrical Shock Dynamics (GSD) theory. GSD has been successfully applied to various gas dynamics problems, and here we have…
In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…
The Hugoniot curves for shock-compressed molybdenum with initial porosities of 1.0, 1.26, 1.83, and 2.31 are theoretically investigated. The method of calculations combines the first-principles treatment for zero- and finite-temperature…
A quantum-mechanical Gaussian wave-packet approach to the theoretical description of nuclear motions in a condensed-phase environment is developed. General expressions for the time-dependent reduced density matrix are given for a harmonic…
We report results of molecular dynamics simulation of shock wave propagation in silicon in [100], [110], and [111] directions obtained using a classical environment-dependent interatomic potential (EDIP). Several regimes of materials…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally…