mlsanityData to 7 Oct 2026

Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks

arXiv 2211.08761 ↗First posted 16 Nov 2022cs.LGcited by 5

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Abstract (arXiv)

Physics-informed neural networks (PINNs) have emerged as new data-driven PDE solvers for both forward and inverse problems. While promising, the expensive computational costs to obtain solutions often restrict their broader applicability. We demonstrate that the computations in automatic differentiation (AD) can be significantly reduced by leveraging forward-mode AD when training PINN. However, a naive application of forward-mode AD to conventional PINNs results in higher computation, losing its practical benefit. Therefore, we propose a network architecture, called separable PINN (SPINN), which can facilitate forward-mode AD for more efficient computation. SPINN operates on a per-axis basis instead of point-wise processing in conventional PINNs, decreasing the number of network forward passes. Besides, while the computation and memory costs of standard PINNs grow exponentially along with the grid resolution, that of our model is remarkably less susceptible, mitigating the curse of dimensionality. We demonstrate the effectiveness of our model in various PDE systems by significantly reducing the training run-time while achieving comparable accuracy. Project page: https://jwcho5576.github.io/spinn/

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 34 of its 48 references that are in the map. First posted on arXiv 16 Nov 2022.

Builds on

34 of 48 references.

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22 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 0; 2025: 0; 2026: 1.

5 papers.

  1. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 78
  2. 2023Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel enginescited by 6
  3. 2023Grad-Shafranov equilibria via data-free physics informed neural networkscited by 5
  4. 2023Learning characteristic parameters and dynamics of centrifugal pumps under multiphase flow using physics-informed neural networkscited by 2
  5. 2026Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solverscited by 0