The goal of this paper is to assess the utility of Reduced-Order Models (ROMs) developed from 3D physics-based models for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for uncertainties in the subsurface system and site-specific details. Numerical simulations…
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Efficiently constructs sparse ROMs for high-dimensional data using causation entropy.
problem Creating effective reduced-order models for high-dimensional dynamical data.
method Uses causation entropy to identify important terms and construct ROMs with varying sparsity.
result Demonstrates the effectiveness of causation entropy in constructing sparse ROMs for chaotic systems with skewed statistics.
Framework improves data-driven ROMs for complex systems using Bayesian operator inference.
problem Improving the quality of data-driven reduced-order models for complex dynamical systems.
method Develops an active learning framework using Bayesian operator inference to identify and select training parameters.
result The proposed adaptive sampling strategy consistently yields more stable and accurate ROMs than random sampling.
This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method combines the perspectives of model reduction and machine learning. Model reduction brin…
Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulationphysics.comp-ph
A novel algorithm uses Gaussian process regression to interpret non-intrusive ROMs.
problem Lack of interpretability in non-intrusive ROMs.
method Latent-space interpolation using Gaussian process regression.
result Interpretability of ROMs improved with continuous time evolution.
This work proposes a novel method for interpolating ROMs without solving FEM models.
problem Interpolating ROMs for unseen parameter values without solving FEM models.
method Non-intrusive Space-Time POD interpolation on compact Stiefel manifolds.
result Robust ROMs derived for unseen parameter values with strong correlations to high-fidelity simulations.
ROM-net framework applies to industrial design uncertainty quantification.
problem Uncertainty quantification in industrial design models.
method Dictionary-based ROM-net framework for reduced order modeling.
result ROM-net computes predictions in 2 hours with high accuracy.
This work develops fast and accurate ROMs for AM models using OL methods.
problem Achieving specific material properties in AM by manipulating process parameters increases computational load.
method Operator learning (OL) approach with Fourier neural operator (FNO) and DeepONet.
result OL methods offer comparable performance and outperform DNN in accuracy and generalizability.
CD-ROM: Complemented Deep-Reduced Order Modelphysics.flu-dyn
A new method uses neural networks to improve POD-Galerkin models for complex systems.
problem Improving computational efficiency and accuracy in solving non-linear high-dimensional systems.
method Deep learning-based closure modeling using neural networks to approximate POD-Galerkin operators.
result The CD-ROM approach produces more accurate and stable models for complex systems.
Enhanced autoencoders improve ROMs for PDEs by capturing essential properties.
problem Autoencoders struggle to capture essential properties for accurate ROMs.
method Introduced symmetric Convolutional AutoEncoders (CAEs) that preserve manifold properties.
result Symmetric CAEs yield more accurate latent trajectories and robust models.
Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Modelsphysics.comp-ph
This paper accelerates inverse solutions for PDEs using ML and ROMs.
problem Efficiently solving inverse problems governed by PDEs with many forward model solves.
method Combining ML with ROMs to improve accuracy and speed.
result ML-enhanced ROMs accelerate inverse problem solving.
This work develops a fast-running ROM for MOOSE-based AM model using OL.
problem Achieving desired material properties in real-time manufacturing processes.
method Operator learning (OL) and Fourier neural operator for ROM development.
result OL-based ROM outperforms conventional deep neural network-based ROM in benchmark tests.
This paper proposes a new method to adapt ROMs for new parameter settings.
problem ROMs lack robustness when applied to new parameter settings.
method Regression trees on Grassmann Manifold to learn the mapping between parameters and POD bases.
result The proposed method is capable of establishing the mapping between parameters and POD bases, thus adapting ROMs for new parameters.
Generative network integrates into ROM for PDEs, matching measurements and estimating uncertainties.
problem Predicting and quantifying uncertainties in numerical simulations of PDEs.
method Generative network (GN) integrated into a reduced-order model (ROM) framework for inverse problems.
result GN-based ROM efficiently quantifies uncertainty and matches measurements with high accuracy.
Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order model (ROM) of an advection-dominated partial differential equation. This is mo…
Adapts POD basis for parametric ROMs using pGP.
problem Updating POD basis for accurate system behavior over parameter space.
method Formulates problem as supervised statistical learning, uses pGP to learn mapping between parameter space and Grassmann manifold.
result Proposes pGP for optimal estimation of POD basis parameters and quantifies uncertainty.
Enhances ROM simulation for multivariate systems with exact Kollo skewness.
problem Modeling multivariate systems with high dimensions and specific higher moments.
method Extends Random Orthogonal Matrix simulation to match target Kollo skewness.
result Established conditions and developed a general approach for constructing admissible values.
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference di…
A Gaussian Process Ordinary Differential Equation framework for large continuous dynamical systems
problem Forecasting complex dynamical systems
method Kernel autonomous ODE approach based on Gaussian Processes and Quadratic Order Model Reduction
result Full model outperforms ROM methods in terms of accuracy or computational costs
Improved latent dynamics identification framework reduces training time and improves accuracy.
problem Accurate numerical solutions of partial differential equations require computationally expensive solvers.
method Sequential decoder training (mLaSDI) to correct residual errors from previous stages.
result mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time.
Method learns latent dynamics of complex systems from noisy data.
problem Challenging to construct ROMs from noisy high-dimensional data.
method Recurrent stochastic variational deep kernel learning (SVDKL).
result Framework accurately predicts system evolution in low-dimensional latent spaces.
This work ensures stability in POD basis interpolation for pMOR in hyperelasticity.
problem Stability of POD basis interpolation on Grassmann manifolds for pMOR in hyperelasticity.
method Stability conditions derived from Grassmannian Exponential map and principal angles.
result Explicit stability conditions for practical pMOR applications and non-monotonic error behavior.
Deep learning has demonstrated success in many applications; however, their use in healthcare has been limited due to the lack of transparency into how they generate predictions. Algorithms such as Recurrent Neural Networks (RNNs) when applied to Electronic Medical Records (EMR) introduce additional barriers to transpa…
DA-PredGAN uses GANs for accurate COVID-19 spread predictions and data assimilation.
problem Predicting and understanding the spread of COVID-19.
method Generative adversarial network (GAN) for predictions and data assimilation.
result DA-PredGAN accurately predicts and assimilates COVID-19 spread data.
Standard micro-economics concentrate on the description of markets but is seldom interested in production. Several economists discussed the concept of a firm, as opposed to an open labour market where entrepreneurs would recrute workers on the occasion of each business opportunity. Coase \cite{Coase} is one of them, wh…
Graph-Laplacians and their spectral embeddings play an important role in multiple areas of machine learning. This paper is focused on graph-Laplacian dimension reduction for the spectral clustering of data as a primary application. Spectral embedding provides a low-dimensional parametrization of the data manifold which…