mlsanityData to 14 Oct 2026

MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problems

arXiv 2204.03193 ↗First posted 7 Apr 2022stat.ML cs.LGcited by 13

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Abstract (arXiv)

A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator network(DeepONet) has been proposed recently for operator learning. Compared to other neural networks to learn functions, it aims at the problem of learning nonlinear operators. However, it can be challenging by using the original model to learn nonlinear operators for high-dimensional stochastic problems. We propose a new multi-resolution autoencoder DeepONet model referred to as MultiAuto-DeepONet to deal with this difficulty with the aid of convolutional autoencoder. The encoder part of the network is designed to reduce the dimensionality as well as discover the hidden features of high-dimensional stochastic inputs. The decoder is designed to have a special structure, i.e. in the form of DeepONet. The first DeepONet in decoder is designed to reconstruct the input function involving randomness while the second one is used to approximate the solution of desired equations. Those two DeepONets has a common branch net and two independent trunk nets. This architecture enables us to deal with multi-resolution inputs naturally. By adding L1 regularization to our network, we found the outputs from the branch net and two trunk nets all have sparse structures. This reduces the number of trainable parameters in the neural network thus making the model more efficient. Finally, we conduct several numerical experiments to illustrate the effectiveness of our proposed MultiAuto-DeepONet model with uncertainty quantification.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Builds on 21 of its 64 references that are in the map. First posted on arXiv 7 Apr 2022.

Builds on

21 of 64 references.

References · 21

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 819
  4. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 262
  5. 2015Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understandingcited by 218
  6. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  7. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  8. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 184
  9. 2019Neural Jump Stochastic Differential Equationscited by 150
  10. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 147
  11. 2018Evaluating Bayesian Deep Learning Methods for Semantic Segmentationcited by 143
  12. 2017Machine Learning of Linear Differential Equations using Gaussian Processescited by 140
9 more
  1. 2017Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activationscited by 104
  2. 2020Local Extreme Learning Machines and Domain Decomposition for Solving Linear and Nonlinear Partial Differential Equationscited by 81
  3. 2017Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equationscited by 72
  4. 2020SpinalNet: Deep Neural Network with Gradual Inputcited by 40
  5. 2018A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equationscited by 23
  6. 2018Neural-net-induced Gaussian process regression for function approximation and PDE solutioncited by 22
  7. 2019Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea statescited by 12
  8. 2020Bayesian Sparse learning with preconditioned stochastic gradient MCMC and its applicationscited by 6
  9. 2015Enhancing Sparsity of Hermite Polynomial Expansions by Iterative Rotationscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 5; 2024: 2; 2025: 1; 2026: 2.

13 papers.

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  1. 2023The Impact of Large Language Models on Scientific Discovery: a Preliminary Study using GPT-4cited by 112
  2. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 92
  3. 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
  4. 2023Learning in latent spaces improves the predictive accuracy of deep neural operatorscited by 19
  5. 2025Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEscited by 9
  6. 2024Modeling Unknown Stochastic Dynamical System Subject to External Excitationcited by 7
  7. 2022Towards Size-Independent Generalization Bounds for Deep Operator Netscited by 6
  8. 2023Size Lowerbounds for Deep Operator Networkscited by 6
  9. 2024Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systemscited by 5
  10. 2023Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONetscited by 3
  11. 2023DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networkscited by 1
  12. 2026A numerical study into neural network surrogate model performance for uncertainty propagationcited by 0
1 more
  1. 2026Data-driven Effective Modeling of Stochastic Chemical Reaction Networkscited by 0