mlsanityData to 7 Oct 2026

Novel Deep neural networks for solving Bayesian statistical inverse

arXiv 2102.03974 ↗First posted 8 Feb 2021math.NA cs.LG cs.NAcited by 10

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Abstract (arXiv)

We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such problems. However, MCMC techniques are computationally challenging as they require several thousands of forward PDE solves. The goal of this paper is to introduce a fractional deep neural network based approach for the forward solves within an MCMC routine. Moreover, we discuss some approximation error estimates and illustrate the efficiency of our approach via several numerical examples.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 13 of its 53 references that are in the map. First posted on arXiv 8 Feb 2021.

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13 of 53 references.

References · 13

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1 more
  1. 2018Machine Learning of Space-Fractional Differential Equationscited by 12

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Citing papers per year: 2021: 1; 2022: 3; 2023: 4; 2024: 1; 2025: 1.

10 papers.

  1. 2021Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flowscited by 6
  2. 2023Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversioncited by 6
  3. 2022An Optimal Time Variable Learning Framework for Deep Neural Networkscited by 3
  4. 2022NINNs: Nudging Induced Neural Networkscited by 2
  5. 2024Enhanced BPINN Training Convergence in Solving General and Multi-scale Elliptic PDEs with Noisecited by 2
  6. 2022Neural Network Representation of Time Integratorscited by 1
  7. 2023A Note on Dimensionality Reduction in Deep Neural Networks using Empirical Interpolation Methodcited by 1
  8. 2023Epistemic Modeling Uncertainty of Rapid Neural Network Ensembles for Adaptive Learningcited by 1
  9. 2023Time Regularization in Optimal Time Variable Learningcited by 0
  10. 2025OCTANE -- Optimal Control for Tensor-based Autoencoder Network Emergence: Explicit Casecited by 0