mlsanityData to 14 Oct 2026

An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator

arXiv 2210.12177 ↗First posted 21 Oct 2022cs.LG cs.NA math.NAcited by 7

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Abstract (arXiv)

This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a convolutional filter for evaluating derivatives the field variable. The NN captures the time-dynamics in smaller latent space through encoder-decoder layers with a Convolutional Long-short Term Memory (ConvLSTM) layer between them. The ConvLSTM architecture is modified by employing a novel activation function to improve the predictive capability of the learning architecture for physics with periodic behavior. The physics is invoked in the form of governing equations at the output of the NN and in the latent (reduced) space. By considering a few benchmark PDEs, we demonstrate the training performance and extrapolation capability of this novel NN architecture by comparing against Physics Informed Neural Networks (PINN) type solvers. It is more capable of extrapolating the solution for future timesteps than the other existing architectures.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 31 of its 62 references that are in the map. First posted on arXiv 21 Oct 2022.

Builds on

31 of 62 references.

References · 31

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19 more
  1. 2019Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networkscited by 129
  2. 2017A unified deep artificial neural network approach to partial differential equations in complex geometriescited by 122
  3. 2021Parallel Physics-Informed Neural Networks via Domain Decompositioncited by 112
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  5. 2020Neural Networks Fail to Learn Periodic Functions and How to Fix Itcited by 100
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Built on by

Cited by year (2026 to 14 Oct)

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

7 papers.

  1. 2023Rethinking materials simulations: Blending direct numerical simulations with neural operatorscited by 25
  2. 2023Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific MLcited by 8
  3. 2023Physics-informed Convolutional Recurrent Surrogate Model for Reservoir Simulation with Well Controlscited by 4
  4. 2024Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularizationcited by 3
  5. 2025Variational Rank Reduction Autoencoders for Generative Thermal Designcited by 1
  6. 2025UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flowscited by 0
  7. 2026Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEscited by 0