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Found 19 papers, 6 papers with code
Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification
We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quantification (UQ) tasks.
Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification
To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data.
Reliability Analysis of Complex Systems using Subset Simulations with Hamiltonian Neural Networks
We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis.
Physics-Informed Polynomial Chaos Expansions
This paper presents a novel methodology for the construction of physics-informed polynomial chaos expansions (PCE) that combines the conventional experimental design with additional constraints from the physics of the model.
On Active Learning for Gaussian Process-based Global Sensitivity Analysis
We propose a novel strategy for active learning that focuses on resolving the main effects of the Gaussian process (associated with the numerator of the Sobol index) and compare this with existing strategies based on convergence in the total variance (the denominator of the Sobol index).
Learning thermodynamically constrained equations of state with uncertainty
Since there are inherent uncertainties in the calibration data (parametric uncertainty) and the assumed functional EOS form (model uncertainty), it is essential to perform uncertainty quantification (UQ) to improve confidence in the EOS predictions.
Learning in latent spaces improves the predictive accuracy of deep neural operators
Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems.
Active Learning-based Domain Adaptive Localized Polynomial Chaos Expansion
The numerical results show the superiority of the DAL-PCE in comparison to (i) a single global polynomial chaos expansion and (ii) the recently proposed stochastic spectral embedding (SSE) method developed as an accurate surrogate model and which is based on a similar domain decomposition process.
General multi-fidelity surrogate models: Framework and active learning strategies for efficient rare event simulation
The multi-fidelity surrogate is assembled by first applying a Gaussian process correction to each low-fidelity model and assigning a model probability based on the model's local predictive accuracy and cost.
Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference
We propose the use of HNNs for performing Bayesian inference efficiently without requiring numerous posterior gradients.
Bayesian Inference with Latent Hamiltonian Neural Networks
Compared to traditional NUTS, L-HNNs in NUTS with online error monitoring required 1--2 orders of magnitude fewer numerical gradients of the target density and improved the effective sample size (ESS) per gradient by an order of magnitude.
Deep transfer operator learning for partial differential equations under conditional shift
Transfer learning (TL) enables the transfer of knowledge gained in learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labeling, potential computational power limitations, and dataset distribution mismatches.
On the influence of over-parameterization in manifold based surrogates and deep neural operators
In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics.
A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems
Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e. g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges.
Reliability Estimation of an Advanced Nuclear Fuel using Coupled Active Learning, Multifidelity Modeling, and Subset Simulation
However, TRISO failure probabilities are small and the associated computational models are expensive.
Data-driven Uncertainty Quantification in Computational Human Head Models
This framework is demonstrated on a 2D subject-specific head model, where the goal is to quantify uncertainty in the simulated strain fields (i. e., output), given variability in the material properties of different brain substructures (i. e., input).
Grassmannian diffusion maps based surrogate modeling via geometric harmonics
Using this representation, geometric harmonics, an out-of-sample function extension technique, is employed to create a global map from the space of input parameters to a Grassmannian diffusion manifold.
Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models
For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner.
Probabilistic modeling of discrete structural response with application to composite plate penetration models
This enables the computationally feasible generation of the probabilistic velocity response (PVR) curve or the $V_0-V_{100}$ curve as a function of the impact velocity, and the ballistic limit velocity prediction as a function of the model parameters.
