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Physics-informed neural networks (PINNs) have emerged as new data-driven PDEsolvers for both forward and inverse problems. While promising, the expensivecomputational costs to obtain solutions often restrict their broaderapplicability. We demonstrate that the computations in automaticdifferentiation (AD) can be significantly reduced by leveraging forward-mode ADwhen training PINN. However, a naive application of forward-mode AD toconventional 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. SPINNoperates on a per-axis basis instead of point-wise processing in conventionalPINNs, decreasing the number of network forward passes. Besides, while thecomputation and memory costs of standard PINNs grow exponentially along withthe grid resolution, that of our model is remarkably less susceptible,mitigating the curse of dimensionality. We demonstrate the effectiveness of ourmodel in various PDE systems by significantly reducing the training run-timewhile achieving comparable accuracy. Project page:https://jwcho5576.github.io/spinn/

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