<p>Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations by embedding governing laws into neural surrogates, but standard single-network PINNs often struggle on multi-domain problems with discontinuous coefficients and interface constraints. Domain-decomposed PINNs alleviate this difficulty by training separate subnetworks per subdomain, yet they introduce redundant feature learning and increased computational cost. This paper proposes a Shared-Trunk Physics-Informed Neural Network (ST-PINN) that combines a single global feature-extraction trunk with lightweight subdomain-specific heads, enabling shared representations across subdomains. To promote physically consistent coupling, an interface-aware loss is introduced to enforce continuity of both the solution and the normal flux across material interfaces. Numerical experiments on representative 1D, 2D, and 3D benchmark problems with known interfaces show that ST-PINN achieves accuracy comparable to or better than conventional PINNs and domain-decomposed baselines while using fewer trainable parameters and generally lower training cost. These results suggest that shared-representation architectures can provide an efficient and accurate approach for benchmark multi-domain PDEs with known interfaces.</p>

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ST-PINN: shared-trunk PINNs for discontinuous multi-domain PDEs

  • Duc Tien Nguyen,
  • Hang Tran,
  • Vu Linh Nguyen

摘要

Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations by embedding governing laws into neural surrogates, but standard single-network PINNs often struggle on multi-domain problems with discontinuous coefficients and interface constraints. Domain-decomposed PINNs alleviate this difficulty by training separate subnetworks per subdomain, yet they introduce redundant feature learning and increased computational cost. This paper proposes a Shared-Trunk Physics-Informed Neural Network (ST-PINN) that combines a single global feature-extraction trunk with lightweight subdomain-specific heads, enabling shared representations across subdomains. To promote physically consistent coupling, an interface-aware loss is introduced to enforce continuity of both the solution and the normal flux across material interfaces. Numerical experiments on representative 1D, 2D, and 3D benchmark problems with known interfaces show that ST-PINN achieves accuracy comparable to or better than conventional PINNs and domain-decomposed baselines while using fewer trainable parameters and generally lower training cost. These results suggest that shared-representation architectures can provide an efficient and accurate approach for benchmark multi-domain PDEs with known interfaces.