Paper tackles uncertainties in reduced-order modeling of complex systems.
problem Model-form uncertainties in reduced-order modeling of complex systems.
method Combines Riemannian projection and retraction operators on a subset of the Stiefel manifold with an information-theoretic formulation.
result Identifies and quantifies the impact of model-form uncertainties on inferred operators.
New method calibrates stochastic reduced-order models from data efficiently.
problem Challenges in estimating drift and diffusion coefficients from data for high-dimensional systems.
method Uses a novel relationship between conditional score and transition density to constrain model coefficients directly from finite-lag statistics.
result Validated on various systems, the method reproduces statistical and dynamical properties of the original models.
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…
This paper presents a technique for reduced-order Markov modeling for compact representation of time-series data. In this work, symbolic dynamics-based tools have been used to infer an approximate generative Markov model. The time-series data are first symbolized by partitioning the continuous measurement space of the …
Paper uses autoencoders for efficient reduced-order modeling of eigenvalue problems.
problem Efficiently modeling eigenvalue problems in high dimensions.
method Autoencoder-based reduced-order modeling for eigenvalue problems.
result Autoencoder-based models outperform standard POD-Galerkin methods in neutron diffusion applications.
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 presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a distribution over the true error. The variance of this distribution can be…
In this work, we develop an importance sampling estimator by coupling the reduced-order model and the generative model in a problem setting of uncertainty quantification. The target is to estimate the probability that the quantity of interest (QoI) in a complex system is beyond a given threshold. To avoid the prohibiti…
Novel hybrid modeling combines ML and physics for real-time diagnosis.
problem Real-time diagnosis of complex systems.
method Combines machine learning and physics-based models to create reduced-order models.
result Generated models are two orders of magnitude simpler, improving efficiency.
Framework predicts nonlinear system responses using GFDT and generative models.
problem Predicting higher-order moments of nonlinear stochastic systems to small perturbations.
method Combining GFDT with generative modeling to estimate score function directly from data.
result Accurately captures nonlinear and non-Gaussian features of system responses.
This research creates efficient models for cyclo-stationary systems using generative methods.
problem Efficiently modeling systems with periodic forcing.
method Score-based generative modeling for reduced-order models.
result Accurately reproduces statistical properties and temporal correlations of cyclo-stationary time series.
New method speeds up deep neural networks inference.
problem Inference speed of deep neural networks.
method Maximum volume algorithm for reduced-order modeling.
result Convolutional layers can be replaced with smaller fully-connected layers with minimal accuracy loss.
The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly …
A new method predicts non-Markovian closure terms for complex systems.
problem Predicting the effect of unresolved variables on resolved dynamics in high-dimensional systems.
method Mamba-Assisted Closure (MAC) framework: sequence model trained to predict closure from resolved trajectory, coupled with reduced-order equations.
result Substantially outperforms existing methods in predictive accuracy and long-time stability.
BayPOD-AL learns reduced-order models from high-fidelity data efficiently.
problem Capturing dynamics of complex systems with large training datasets.
method Bayesian active learning based on uncertainty-aware POD.
result BayPOD-AL reduces computational cost and improves model accuracy.
This work proposes a model for geodesic distances and flows on manifolds.
problem Geodesic distances and flows on differentiable manifolds.
method Manifold-augmented Eikonal equation solutions.
result Geodesic flow provides globally length-minimizing curves.
New method approximates controllability of large networks from coarse summaries.
problem Controlling large-scale linear dynamical systems with incomplete network information.
method Algorithm using stochastic block model to estimate controllability from coarse summaries.
result Average controllability of fine-scale system can be well approximated by coarse-scale system.
New method learns nonlinear projections for reduced-order modeling of complex dynamical systems.
problem Modeling transient dynamics near a manifold in nonlinear systems.
method Constrained autoencoder neural networks with invertible activation functions and biorthogonal weight matrices.
result Demonstrated effectiveness on a vortex shedding model, learning oblique fibers for fast dynamics.
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.
Machine learning improves combustion system predictions by integrating physical models.
problem Improving accuracy of complex multi-physics systems like combustion.
method Coupling machine learning algorithms with physical models and constraints.
result Enhanced predictive capabilities in turbulent combustion.
ROAD-EnKFs use learned low-dimensional models to improve state reconstruction and forecasting.
problem Reconstructing and forecasting states of unknown or expensive systems.
method Learned low-dimensional surrogate models and ensemble Kalman filter integration.
result ROAD-EnKFs achieve higher accuracy at lower computational cost than existing methods.
Framework detects tipping points in complex systems using ML.
problem Detecting tipping points in complex, emergent systems.
method Combining manifold learning, neural networks, and Gaussian processes.
result Reduced-order models for mesoscopic and mean-field dynamics.
Paper uses neural networks to speed up simulations of complex systems.
problem Rapid simulations of advection-dominated problems in engineering and geophysics.
method Recurrent neural network for approximating nonlinear component of ROM.
result The proposed framework accurately recovers transient dynamics without full nonlinear computations.
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical interest is computationally infeasible or impractical. In complex systems, with lim…
Reduced-order model improves LES for atmospheric pollutant dispersion.
problem Accurate near-field pollutant concentration tracking in urban areas.
method Combining POD and GPR for non-intrusive reduced-order modeling.
result Component-by-component optimization captures spatial scales in high-order modes.
GenUQ uses generative models to estimate uncertainty in operator learning.
problem Uncertainty quantification in stochastic operator models.
method Introduces a measure-theoretic approach with a generative hyper-network.
result Outperforms other UQ methods in various example problems.
Study reduces financial dynamics complexity using PCA for NASDAQ, oil, gold, and USD.
problem Understanding complex financial interactions among multiple assets.
method Time-delay embedding and PCA for dimensionality reduction, followed by linear regression.
result Limited number of principal components capture dominant dynamics of each asset.
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.
Bayesian method improves forecasting of nonseparable Hamiltonian systems with noise.
problem Forecasting nonseparable Hamiltonian systems with multiplicative noise.
method Bayesian approach using deep learning and reduced-order modeling.
result Bayesian method yields up to 724 times improvement in forecasting accuracy.
In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem. In addition to the ML algorithms…
Gravitational-wave data analysis is rapidly absorbing techniques from deep learning, with a focus on convolutional networks and related methods that treat noisy time series as images. We pursue an alternative approach, in which waveforms are first represented as weighted sums over reduced bases (reduced-order modeling)…
New method for decomposing high-dimensional parametric domains using PCA and inverse projection.
problem Decomposing high-dimensional parametric domains efficiently.
method Iterative Principal Component Analysis (PCA) and inverse projection methods.
result The proposed method effectively reconstructs the original domain from lower-dimensional data.
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.
Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Reg…
Active sampling selects few points for accurate model reduction of high-fidelity systems.
problem Efficiently identify dominant subspaces for model reduction of large training sets.
method Proposes an active sampling strategy to select a few points from the training set to estimate dominant subspaces accurately.
result Active sampling can provide 17x speed-up without sacrificing accuracy.
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.
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.
AI learns reduced-order models for computational science.
problem Discovering efficient reduced-order models for complex simulations.
method Reinforcement learning framework to discover models expressed in analytical form, evaluated a posteriori, and guided by integral quantities.
result AI discovers interpretable models for specific solvers, improving efficiency and accuracy.
Optimized DMD for fast atmospheric chemistry forecasting.
problem Forecasting global atmospheric chemistry dynamics efficiently.
method Optimized Dynamic Mode Decomposition (DMD) for reduced order modeling.
result Significant improvement in computational speed and interpretability.
Direct numerical simulation of Stokes flow through an impermeable, rigid body matrix by finite elements requires meshes fine enough to resolve the pore-size scale and is thus a computationally expensive task. The cost is significantly amplified when randomness in the pore microstructure is present and therefore multipl…
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.
Enhanced probabilistic sampling on manifolds using Double Diffusion Maps and Geometric Harmonics.
problem Overfitting and loss of generalization in PLoM when N is small and dimensionality approaches N.
method Extending PLoM with Double Diffusion Maps and Geometric Harmonics to handle small N and high-dimensional data.
result Effective and robust method for generating statistically consistent realizations from limited data.
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.
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.
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.
Reduced order modeling of energetic materials using physics-aware neural networks.
problem Simulating complex spatiotemporal dynamics in energetic materials.
method Physics-aware recurrent convolutions (PARC) combined with latent space projection to accelerate model training and inference.
result Significant decrease in training and inference time with comparable accuracy.
Algorithm learns latent variables for thermodynamically-consistent deep neural networks.
problem Predicting time evolution of large-scale physical systems with thermodynamic consistency.
method Sparse autoencoders and structure-preserving neural networks.
result Method conserves total energy and entropy inequality for both conservative and dissipative systems.
Proposes an online method for high-dimensional streaming data.
problem Increasing variable dimensions with sample size in online kernel sliced inverse regression.
method Introduces approximate linear dependence condition and dictionary variable sets to address the problem. Transforms into online generalized eigen-decomposition problem and uses stochastic optimization for updates.
result Achieves close performance to batch processing kernel sliced inverse regression.