PPPD framework extracts physical characterizations from stochastic mechanical systems.
problem Complex system behavior requires more than probabilistic descriptions of QoI.
method Probabilistic Performance-Pattern Decomposition (PPPD) framework.
result Decomposes system behaviors into meaningful patterns in response space.
Bayesian SDOE method estimates QoIs from expensive black-box functions efficiently.
problem Estimating non-linear QoIs from expensive, unknown functions.
method Sequential design of experiments using Bayesian surrogate models and information gain.
result Method efficiently estimates QoIs with limited function evaluations.
Bayesian optimal design of experiments (BODE) has been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific designs selected by an infill-sampling criterion. However, most current BODE method…
LUQ learns QoI from dynamical systems for consistent observation inversion.
problem Quantifying uncertainties on model inputs corresponding to observable QoI in dynamical systems.
method LUQ framework for SIPs, including data filtering, dynamics learning, observation classification, and feature extraction.
result LUQ provides tractable solutions to SIPs for dynamical systems, enabling uncertainty quantification.
BF-VAE estimates uncertainty from LF and HF QoI samples.
problem Balancing computational efficiency and numerical accuracy in uncertainty quantification.
method Bi-fidelity formulation of VAEs in latent space.
result BF-VAE improves accuracy with limited HF data.
Framework combines machine learning and inverse methods to quantify uncertainties in model parameters.
problem Combining aleatoric and epistemic uncertainties in engineered systems modeling.
method Develops a robust filtering step in LUQ to learn useful QoI maps from noisy datasets, iterates over time, and uses sufficiency tests.
result Transforms datasets into distributions for DC-based inversion, improving parameter quantification.
Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between processes on these two scales is essential to both the derivation of macroscopic models of, e.g., transport phenomena in natural porous media,…
GO-OED maximizes predictive information gain on nonlinear QoIs.
problem Maximizing information gain on nonlinear predictive quantities.
method Nested Monte Carlo estimator, Markov chain Monte Carlo, kernel density estimation, Bayesian optimization.
result GO-OED outperforms conventional OED in nonlinear settings.
GINNs combine deep learning with PGMs for physics-based multiscale systems.
problem Intrinsic computational bottlenecks and lack of sufficient data for QoI estimation.
method Hybrid approach combining deep learning with probabilistic graphical models, informed by structured priors for CVs.
result GINNs produce tight confidence intervals for non-Gaussian QoIs.
Machine learning models accurately predict the state and dynamics of reactive mixing.
problem Accurate prediction of reactive mixing for Earth and environmental science applications.
method Built a high-fidelity numerical model to simulate reactive mixing scenarios. Used 20 different machine learning emulators to classify mixing state and predict three QoIs.
result Ensemble methods and MLP models accurately predict the state of reactive mixing and QoIs, significantly faster than high-fidelity simulations.
This paper analyzes uncertainty in DFN simulations using sensitivity analysis.
problem Uncertainty in estimating QoI due to epistemic and aleatoric uncertainties in DFN simulations.
method Sensitivity analysis to attribute uncertainty to input parameters and aleatoric uncertainty.
result Characterizes uncertainty in DFN flow simulations with heteroskedastic aleatoric uncertainty.
We propose a new forecasting method for predicting load demand and generation scheduling. Accurate week-long forecasting of load demand and optimal power generation is critical for efficient operation of power grid systems. In this work, we use a synthetic data set describing a power grid with 700 buses and 134 generat…
A new method for experimental design focuses on predicting downstream quantities of interest.
problem Designs that maximize parameter learning may not maximize downstream quantity prediction.
method Likelihood-free goal-oriented optimal experimental design (LF-GO-OED) using ABC density ratio estimation.
result LF-GO-OED maximizes the expected information gain for downstream quantities.
Paper integrates real data into probabilistic models using Fourier transform.
problem Learning from constrained data sets in high dimensions.
method Functional approach based on weak formulation of Fourier transform of probability measures.
result Estimation of posterior probability measures for QoI and QoI with control parameter.
This paper introduces a method for efficiently inferring a high-dimensional distributed quantity from a few observations. The quantity of interest (QoI) is approximated in a basis (dictionary) learned from a training set. The coefficients associated with the approximation of the QoI in the basis are determined by minim…
Enhanced Gaussian process regression for multi-fidelity data fusion.
problem Combining data of varying fidelity levels for accurate predictions.
method Gradient-enhanced Cokriging method (GE-Cokriging) for QoI and its gradients.
result GE-Cokriging outperforms conventional multi-fidelity Cokriging in predicting QoI and gradients.
Improved surrogate model for field-valued QoIs using LF and HF simulations.
problem Accurate and efficient modeling of field-valued quantities under uncertain inputs.
method Bifidelity Karhunen-Loève expansion with active learning.
result Consistent improvements in predictive accuracy and sample efficiency.
ITF improves DSR but inflates curvature, while marginal likelihood reduces it, affecting QoIs.
problem Curvature mismatch between teacher forcing and marginal likelihood in chaotic dynamical systems.
method Comparing objective-induced curvatures of ITF and marginal likelihood in a probabilistic switching augmentation of AL-RNNs.
result Curvature inflation by ITF and reduction by marginal likelihood affect dynamical quantities of interest.
Develops a method to explain deep learning models for complex systems.
problem Rapid simulation-based prototyping of complex systems with high-dimensional CVs and QoIs.
method Moment-independent global sensitivity analysis using differential mutual information.
result Surrogate model driven by mutual information provides useful rankings and optimizations.
Surrogate model construction for vector-valued outputs
problem Improving surrogate model accuracy and stability for complex engineering systems
method Adaptive sequential sampling for polynomial chaos expansion
result Improves surrogate accuracy and stability
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…
Improves inverse uncertainty quantification for time-dependent data using PCA and deep neural networks.
problem Efficiently quantify model input uncertainties from time-dependent experimental data.
method Functional PCA for dimensionality reduction, deep neural networks for surrogate modeling, Bayesian neural networks for uncertainty estimation.
result The proposed method reduces the computational cost and improves the agreement with experimental data.
The paper discusses scalable learning for wireless data-driven systems.
problem Expanding data volume and model complexity limit centralized learning solutions.
method Discusses scalable architecture and local learning strategies.
result Promising research directions in scalable data-driven wireless communications.
This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential r…
Optimal data-driven formulations are found for learning and decision-making with historical data.
problem Designing optimal learning and decision-making formulations from historical data.
method Define a yardstick for measuring formulation quality, then construct an optimal formulation that is uniformly closer to the true cost.
result Existence of three distinct out-of-sample performance regimes with corresponding optimal formulations.
A new method for support vector regression using a data-driven insensitive parameter.
problem Determining an optimal insensitive parameter in support vector regression.
method A data-driven approach to approximate the insensitive parameter by minimizing a generalized loss function based on the likelihood principle.
result The proposed method outperforms traditional support vector regression methods and has lower computational costs.
WeatherBench provides a dataset and metrics for comparing data-driven weather forecasts.
problem Lack of a common dataset and evaluation metrics for data-driven weather forecasting.
method Publicly available dataset derived from ERA5, simple evaluation metrics.
result Baseline scores from various forecasting methods provided for comparison.
Paper presents a data-driven method for option pricing.
problem Option pricing accuracy under market volatility.
method Data-driven ensemble approach based on no-arbitrage theory.
result Model performance validated with real data.
Proposes data-driven methods for estimating conditional expectations.
problem Estimating conditional expectations when underlying density is unknown.
method Data-driven techniques to directly estimate conditional expectations from training data.
result Extends data-driven method to solve nonlinear equations in stochastic optimization.
Hybridizes physical and data-driven methods for predicting physicochemical properties.
problem Predicting physicochemical properties accurately using limited data.
method Distills physical method predictions into a prior model and combines with sparse experimental data using Bayesian inference.
result Significant improvements in predicting activity coefficients at infinite dilution compared to baselines and ensemble methods.
This research designs a data-driven partition to test independence between continuous variables.
problem Testing independence between continuous random variables.
method Empirical log-likelihood statistic and data-driven tree-structured partition.
result Strongly consistent test of independence over probability families.
Data-driven method for option pricing using historical asset prices.
problem Tackling the gap between historical asset prices and risk-neutral option pricing.
method Identifying a pricing kernel process, solving utility maximization and functional optimization problems using deep learning.
result Demonstrated the efficiency of the data-driven option pricing methodology.
We study the performance of data-driven, a priori and random approaches to label space partitioning for multi-label classification with a Gaussian Naive Bayes classifier. Experiments were performed on 12 benchmark data sets and evaluated on 5 established measures of classification quality: micro and macro averaged F1 s…
Study integrates machine learning with SAA for optimizing decisions based on uncertain parameters and covariates.
problem Optimizing decisions under uncertain parameters and covariates.
method Data-driven frameworks integrating machine learning prediction models within SAA for scenario generation.
result Consistent and asymptotically optimal solutions under certain conditions, with finite sample guarantees.
New tool improves scalability of data-driven invariant inference.
problem Scaling data-driven invariant inference to programs with many variables.
method Developed oasis tool to improve scalability.
result Outperforms state-of-the-art systems on benchmarks.
New framework for data-driven hyperparameter tuning with structured loss.
problem Statistical foundations for multi-dimensional hyperparameter tuning remain limited.
method General framework using real algebraic geometry for semi-algebraic function classes.
result First general guarantees for multi-dimensional hyperparameter tuning.
Data-driven approach learns effective equations for phase field interfaces.
problem Learning accurate equations for phase field interface dynamics.
method Data-driven identification of partial differential equations from phase field data.
result Data-driven equations outperform analytical approximations in certain regimes.
Data-driven models analyze power grids under incomplete physical information, and their accuracy has been mostly validated empirically using certain training and testing datasets. This paper explores error bounds for data-driven models under all possible training and testing scenarios, and proposes an evaluation implem…
RCUKF combines data-driven modeling and Bayesian estimation for accurate system state estimation.
problem Challenges in obtaining reliable process models for complex systems.
method Integrates reservoir computing with unscented Kalman filtering.
result Demonstrated effectiveness on benchmark problems and real-time vehicle trajectory estimation.
Stochastic cutting planes improve data-driven optimization speed.
problem Data-driven Mixed-Integer Nonlinear Optimization problems.
method Stochastic version of cutting-plane method.
result Stochastic algorithm converges to ε-optimal solution with high probability.
Most structure inference methods either rely on exhaustive search or are purely data-driven. Exhaustive search robustly infers the structure of arbitrarily complex data, but it is slow. Data-driven methods allow efficient inference, but do not generalize when test data have more complex structures than training data. I…
Machine learning finds new natural laws from noisy data.
problem Discovery of natural laws relies on human inspiration.
method Recursive-LASSO-based symbolic regression (RLS) method.
result Data-driven formulation of natural laws from noisy data.
Data-driven Distributionally Robust Optimization (DD-DRO) via optimal transport has been shown to encompass a wide range of popular machine learning algorithms. The distributional uncertainty size is often shown to correspond to the regularization parameter. The type of regularization (e.g. the norm used to regularize)…
GNPs learn operators on non-Euclidean geometries using neural networks.
problem Learning operators on complex geometries like manifolds.
method Geometric Neural Operators (GNPs) that incorporate geometric properties.
result GNPs can estimate metrics, solve PDEs, and learn LB operators on manifolds.
Develops theory for data-driven methods in dynamical systems.
problem Lack of analysis for data-driven methods in dynamical systems.
method Establishes existence of mapping and properties of operator learning architecture.
result Novel universal approximation theorems for smoothing and forecasting.
This paper analyzes data-driven Newsvendor problems and finds a wide range of possible regrets.
problem Guessing the number drawn from an unknown distribution with asymmetric costs.
method Unified analysis using the notion of clustered distributions and new lower bounds.
result The entire spectrum of achievable regrets from 1 / n 1/\sqrt{n} 1/ n to 1 / n 1/n 1/ n is possible. The MEM method uses data-driven priors for linear inverse problems, proving convergence and estimating differences.
problem Linear inverse problems with approximate priors.
method Maximum Entropy on the Mean (MEM) method with data-driven priors.
result Empirical mean convergence and estimates for prior differences based on epigraphical distance.
Develops scenario theory for multi-criteria decision making.
problem Need for robustness assessment with multiple criteria and datasets.
method Collectively treats risks associated with individual criteria for multi-criteria decision problems.
result More accurate robustness certificates and sharper quantification of simultaneous criterion satisfaction.