Physics-Informed Neural Networks (PINNs) are a useful framework for approximating partial differential equation solutions using deep learning methods. In this paper, we propose a principled redesign of the PINNsformer, a Transformer-based PINN architecture. We present the Spectral PINNSformer (S-Pformer), a refinement of encoder-decoder PINNSformers that addresses two key issues; 1. the redundancy (i.e. increased parameter count) of the encoder, and 2. the mitigation of spectral bias. We find that the encoder is unnecessary for capturing spatiotemporal correlations when relying solely on self-attention, thereby reducing parameter count. Further, we integrate Fourier feature embeddings to explicitly mitigate spectral bias, enabling adaptive encoding of multiscale behaviors in the frequency domain. Our model outperforms encoder-decoder PINNSformer architectures across all benchmarks, achieving or outperforming MLP performance while reducing parameter count significantly.

Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons (MLP), neglect the crucial temporal dependencies inherent in practical physics systems and thus fail to propagate the initial condition constraints globally and accurately capture the true solutions under various scenarios. In this paper, we introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer can accurately approximate PDE solutions by utilizing multi-head attention mechanisms to capture temporal dependencies. PINNsFormer transforms point-wise inputs into pseudo sequences and replaces point-wise PINNs loss with a sequential loss. Additionally, it incorporates a novel activation function, Wavelet, which anticipates Fourier decomposition through deep neural networks. Empirical results demonstrate that PINNsFormer achieves superior generalization ability and accuracy across various scenarios, including PINNs failure modes and high-dimensional PDEs. Moreover, PINNsFormer offers flexibility in integrating existing learning schemes for PINNs, further enhancing its performance.