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Found 27 papers, 12 papers with code
Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations
Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time.
CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations
This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the evolution of solution fields at new physics parameters and new initial conditions.
Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes
This work focuses on the conservation of quantities such as Hamiltonians, mass, and momentum when solution fields of partial differential equations are approximated with nonlinear parametrizations such as deep networks.
Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networks
Training neural networks sequentially in time to approximate solution fields of time-dependent partial differential equations can be beneficial for preserving causality and other physics properties; however, the sequential-in-time training is numerically challenging because training errors quickly accumulate and amplify over time.
Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matrices
We introduce a multifidelity estimator of covariance matrices formulated as the solution to a regression problem on the manifold of symmetric positive definite matrices.
Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes
Training nonlinear parametrizations such as deep neural networks to numerically approximate solutions of partial differential equations is often based on minimizing a loss that includes the residual, which is analytically available in limited settings only.
Rank-Minimizing and Structured Model Inference
While extracting information from data with machine learning plays an increasingly important role, physical laws and other first principles continue to provide critical insights about systems and processes of interest in science and engineering.
Multi-Fidelity Covariance Estimation in the Log-Euclidean Geometry
We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold.
Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models
Multilevel Stein variational gradient descent is a method for particle-based variational inference that leverages hierarchies of surrogate target distributions with varying costs and fidelity to computationally speed up inference.
Operator inference with roll outs for learning reduced models from scarce and low-quality data
Data-driven modeling has become a key building block in computational science and engineering.
Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification
When training low-fidelity models, the proposed approach takes into account the context in which the learned low-fidelity models will be used, namely for variance reduction in Monte Carlo estimation, which allows it to find optimal trade-offs between training and sampling to minimize upper bounds of the mean-squared errors of the estimators for given computational budgets.
Context-aware controller inference for stabilizing dynamical systems from scarce data
This work introduces a data-driven control approach for stabilizing high-dimensional dynamical systems from scarce data.
Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equations
Neural Galerkin schemes build on the Dirac-Frenkel variational principle to train networks by minimizing the residual sequentially over time, which enables adaptively collecting new training data in a self-informed manner that is guided by the dynamics described by the partial differential equations.
On the sample complexity of stabilizing linear dynamical systems from data
Learning controllers from data for stabilizing dynamical systems typically follows a two step process of first identifying a model and then constructing a controller based on the identified model.
An Extensible Benchmark Suite for Learning to Simulate Physical Systems
Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications.
Active operator inference for learning low-dimensional dynamical-system models from noisy data
Furthermore, the connection between operator inference and projection-based model reduction enables bounding the mean-squared errors of predictions made with the learned models with respect to traditional reduced models.
Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference
Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction).
Multilevel Stein variational gradient descent with applications to Bayesian inverse problems
The proposed multilevel Stein variational gradient descent moves most of the iterations to lower, cheaper levels with the aim of requiring only a few iterations on the higher, more expensive levels when compared to the traditional, single-level Stein variational gradient descent variant that uses the highest-level distribution only.
Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories
The core contributions of this work are a data sampling scheme to sample partially observed states from high-dimensional dynamical systems and a formulation of a regression problem to fit the non-Markovian reduced terms to the sampled states.
Context-aware surrogate modeling for balancing approximation and sampling costs in multi-fidelity importance sampling and Bayesian inverse problems
Thus, there is a trade-off between investing computational resources to improve the accuracy of surrogate models versus simply making more frequent recourse to expensive high-fidelity models; however, this trade-off is ignored by traditional modeling methods that construct surrogate models that are meant to replace high-fidelity models rather than being used together with high-fidelity models.
Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems
Classical reduced models are low-rank approximations using a fixed basis designed to achieve dimensionality reduction of large-scale systems.
Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations
This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs.
Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated in the right-hand side.
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
The lifting map is applied to data obtained by evaluating a model for the original nonlinear system.
BIG-bench Machine Learning
Physics-informed machine learning
Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolation
Loewner rational interpolation provides a versatile tool to learn low-dimensional dynamical-system models from frequency-response measurements.
Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference
Thus, the learned models are guaranteed to inherit the well-studied properties of reduced models from traditional model reduction.
Stabilizing discrete empirical interpolation via randomized and deterministic oversampling
Numerical experiments with synthetic and diffusion-reaction problems demonstrate the stability of oversampled empirical interpolation in the presence of noise.
Numerical Analysis
