Discovering and forecasting extreme events via active learning in neural operators
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Abstract (arXiv)
Extreme events in society and nature, such as pandemic spikes, rogue waves, or structural failures, can have catastrophic consequences. Characterizing extremes is difficult as they occur rarely, arise from seemingly benign conditions, and belong to complex and often unknown infinite-dimensional systems. Such challenges render attempts at characterizing them as moot. We address each of these difficulties by combining novel training schemes in Bayesian experimental design (BED) with an ensemble of deep neural operators (DNOs). This model-agnostic framework pairs a BED scheme that actively selects data for quantifying extreme events with an ensemble of DNOs that approximate infinite-dimensional nonlinear operators. We find that not only does this framework clearly beat Gaussian processes (GPs) but that 1) shallow ensembles of just two members perform best; 2) extremes are uncovered regardless of the state of initial data (i.e. with or without extremes); 3) our method eliminates "double-descent" phenomena; 4) the use of batches of suboptimal acquisition points compared to step-by-step global optima does not hinder BED performance; and 5) Monte Carlo acquisition outperforms standard optimizers in high-dimensions. Together these conclusions form the foundation of an AI-assisted experimental infrastructure that can efficiently infer and pinpoint critical situations across many domains, from physical to societal systems.
Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). Builds on 22 of its 75 references that are in the map. First posted on arXiv 5 Apr 2022.
Builds on
22 of 75 references.
References · 22
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- 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
- 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2017Deep Bayesian Active Learning with Image Datacited by 812
- 2018Evidential Deep Learning to Quantify Classification Uncertaintycited by 728
- 2021A Survey of Uncertainty in Deep Neural Networkscited by 675
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- 2018Predictive Uncertainty Estimation via Prior Networkscited by 555
- 2020A Survey of Deep Active Learningcited by 547
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10 more
- 2021Neural Operator: Learning Maps Between Function Spacescited by 413
- 2017Snapshot Ensembles: Train 1, get M for freecited by 349
- 2019Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Visioncited by 182
- 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 169
- 2019Active Learning for Deep Detection Neural Networkscited by 62
- 2018A sequential sampling strategy for extreme event statistics in nonlinear dynamical systemscited by 14
- 2019Output-weighted optimal sampling for Bayesian regression and rare event statistics using few samplescited by 7
- 2021Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffscited by 5
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Citing papers per year: 2022: 3; 2023: 9; 2024: 5; 2025: 7; 2026: 8.
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- 2022NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operatorscited by 33
- 2023Multi-Resolution Active Learning of Fourier Neural Operatorscited by 22
- 2024Active Learning for Neural PDE Solverscited by 22
- 2023Improved generalization with deep neural operators for engineering systems: Path towards digital twincited by 19
- 2023A Comprehensive Survey on Rare Event Predictioncited by 18
- 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
- 2024Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learningcited by 9
- 2023Stochastic Latent Transformer: Efficient Modelling of Stochastically Forced Zonal Jetscited by 8
- 2022Digital Twin-Centered Hybrid Data-Driven Multi-Stage Deep Learning Framework for Enhanced Nuclear Reactor Power Predictioncited by 6
- 2025Active Learning with Selective Time-Step Acquisition for PDEscited by 4
- 2023Implementation of the Critical Wave Groups Method with Computational Fluid Dynamics and Neural Networkscited by 3
- 2024Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiologycited by 3
20 more
- 2023Learning Functional Transductioncited by 2
- 2023Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systemscited by 2
- 2024Active search for Bifurcationscited by 2
- 2024Evaluating the Role of Data Enrichment Approaches Towards Rare Event Analysis in Manufacturingcited by 2
- 2022Information FOMO: The unhealthy fear of missing out on information. A method for removing misleading data for healthier modelscited by 1
- 2023A Data-Driven Approach to Morphogenesis under Structural Instabilitycited by 1
- 2025Learning where to learn: Training data distribution optimization for scientific machine learningcited by 1
- 2025Thompson Sampling in Function Spaces via Neural Operatorscited by 1
- 2025Banach neural operator for Navier-Stokes equationscited by 1
- 2026Multimodal Scientific Learning Beyond Diffusions and Flowscited by 1
- 2023A generalized likelihood-weighted optimal sampling algorithm for rare-event probability quantificationcited by 0
- 2025BLADE: Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systemscited by 0
- 2025Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertaintycited by 0
- 2026A numerical study into neural network surrogate model performance for uncertainty propagationcited by 0
- 2026Data-Efficient Neural Operator Training via Physics-Based Active Learningcited by 0
- 2026Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projectionscited by 0
- 2026How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limitcited by 0
- 2026A Physics-Informed Neural Network Framework for Elastodynamic Wave Propagation in Bimaterial Systemscited by 0
- 2026Noise-Induced Predictability Redistribution Across Forecast Horizons of Extreme Events in Chaotic Dynamicscited by 0
- 2026Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Eventscited by 0
- 2026Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events25 Sep 2026
- 2026Noise-Induced Predictability Redistribution Across Forecast Horizons of Extreme Events in Chaotic Dynamics20 Aug 2026
- 2026A Physics-Informed Neural Network Framework for Elastodynamic Wave Propagation in Bimaterial Systems7 Jul 2026
- 2026How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit10 Jun 2026
- 2026Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projections4 Jun 2026
- 2026Data-Efficient Neural Operator Training via Physics-Based Active Learning20 May 2026
- 2026A numerical study into neural network surrogate model performance for uncertainty propagation15 May 2026
- 2026Multimodal Scientific Learning Beyond Diffusions and Flows1 Feb 2026
- 2025Banach neural operator for Navier-Stokes equations28 Nov 2025
- 2025Active Learning with Selective Time-Step Acquisition for PDEs22 Nov 2025
- 2025Thompson Sampling in Function Spaces via Neural Operators27 Jun 2025
- 2025Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertainty13 Jun 2025
20 more
- 2025Learning where to learn: Training data distribution optimization for scientific machine learning27 May 2025
- 2025Active operator learning with predictive uncertainty quantification for partial differential equations5 Mar 2025
- 2025BLADE: Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systems4 Mar 2025
- 2024Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology13 Aug 2024
- 2024Active Learning for Neural PDE Solvers2 Aug 2024
- 2024Evaluating the Role of Data Enrichment Approaches Towards Rare Event Analysis in Manufacturing1 Jul 2024
- 2024Active search for Bifurcations17 Jun 2024
- 2024Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning12 Apr 2024
- 2023Stochastic Latent Transformer: Efficient Modelling of Stochastically Forced Zonal Jets25 Oct 2023
- 2023A generalized likelihood-weighted optimal sampling algorithm for rare-event probability quantification22 Oct 2023
- 2023Multi-Resolution Active Learning of Fourier Neural Operators29 Sep 2023
- 2023A Comprehensive Survey on Rare Event Prediction20 Sep 2023
- 2023A Data-Driven Approach to Morphogenesis under Structural Instability23 Aug 2023
- 2023Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems27 Jun 2023
- 2023Learning Functional Transduction1 Feb 2023
- 2023Implementation of the Critical Wave Groups Method with Computational Fluid Dynamics and Neural Networks24 Jan 2023
- 2023Improved generalization with deep neural operators for engineering systems: Path towards digital twin17 Jan 2023
- 2022Digital Twin-Centered Hybrid Data-Driven Multi-Stage Deep Learning Framework for Enhanced Nuclear Reactor Power Prediction23 Nov 2022
- 2022Information FOMO: The unhealthy fear of missing out on information. A method for removing misleading data for healthier models27 Aug 2022
- 2022NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators25 Aug 2022
- 2022NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operatorscited by 33
- 2023Multi-Resolution Active Learning of Fourier Neural Operatorscited by 22
- 2024Active Learning for Neural PDE Solverscited by 22
- 2023Improved generalization with deep neural operators for engineering systems: Path towards digital twincited by 19
- 2023A Comprehensive Survey on Rare Event Predictioncited by 18
- 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
- 2024Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learningcited by 9
- 2023Stochastic Latent Transformer: Efficient Modelling of Stochastically Forced Zonal Jetscited by 8
- 2022Digital Twin-Centered Hybrid Data-Driven Multi-Stage Deep Learning Framework for Enhanced Nuclear Reactor Power Predictioncited by 6
- 2025Active Learning with Selective Time-Step Acquisition for PDEscited by 4
- 2023Implementation of the Critical Wave Groups Method with Computational Fluid Dynamics and Neural Networkscited by 3
- 2024Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiologycited by 3
12 most cited of 32 All 32 (JSON)
- 2026Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events25 Sep 2026
- 2026Noise-Induced Predictability Redistribution Across Forecast Horizons of Extreme Events in Chaotic Dynamics20 Aug 2026
- 2026A Physics-Informed Neural Network Framework for Elastodynamic Wave Propagation in Bimaterial Systems7 Jul 2026
- 2026How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit10 Jun 2026
- 2026Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projections4 Jun 2026
- 2026Data-Efficient Neural Operator Training via Physics-Based Active Learning20 May 2026
- 2026A numerical study into neural network surrogate model performance for uncertainty propagation15 May 2026
- 2026Multimodal Scientific Learning Beyond Diffusions and Flows1 Feb 2026
- 2025Banach neural operator for Navier-Stokes equations28 Nov 2025
- 2025Active Learning with Selective Time-Step Acquisition for PDEs22 Nov 2025
- 2025Thompson Sampling in Function Spaces via Neural Operators27 Jun 2025
- 2025Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertainty13 Jun 2025
12 newest of 32 All 32 (JSON)