Eradicating Negative Transfer in Multi-Physics Foundation Models via Sparse Mixture-of-Experts Routing

TL;DR

This paper introduces Shodh-MoE, a sparse mixture-of-experts neural architecture that effectively separates and learns multiple physics regimes in scientific modeling, reducing negative transfer and improving accuracy.

Contribution

The paper proposes a novel sparse-activated transformer with dynamic routing for multi-physics transport, enabling specialized learning and mitigating interference between different PDE regimes.

Findings

Model achieves exact mass conservation with divergence ~2.8 x 10^-10.

Routing telemetry shows domain-specific expert specialization.

Latent and physical MSEs demonstrate high accuracy across regimes.

Abstract

Scaling Scientific Machine Learning (SciML) toward universal foundation models is bottlenecked by negative transfer: the simultaneous co-training of disparate partial differential equation (PDE) regimes can induce gradient conflict, unstable optimization, and plasticity loss in dense neural operators. In particular, broadband open-channel fluid dynamics and boundary-dominated porous media flows impose incompatible spectral and geometric demands on a single dense parameter path. We introduce Shodh-MoE, a sparse-activated latent transformer architecture for multi-physics transport. Shodh-MoE operates on compressed 16^3 physical latents produced by a physics-informed autoencoder with an intra-tokenizer Helmholtz-style velocity parameterization, restricting decoded states to divergence-free velocity manifolds. The model guarantees exact mass conservation, achieving a physically verifiable velocity divergence of ~2.8 x 10^-10 (evaluated post-hoc in FP64) on 128^3 grids. A Top-1 soft-semantic router dynamically assigns localized latent patches to expert subnetworks, enabling specialized parameter paths for distinct physical mechanisms while preserving shared experts for universal symmetries. In a 20,000-step distributed pretraining run over mixed three-dimensional physical tensors, routing telemetry shows autonomous domain bifurcation: held-out validation tokens from the open-channel domain route exclusively to Expert 0, while porous-media tokens route exclusively to Expert 1. The model converges simultaneously across both regimes, achieving latent validation MSEs of 2.46 x 10^-5 and 9.76 x 10^-6, and decoded physical MSEs of 2.48 x 10^-6 and 1.76 x 10^-6. These results support sparse expert routing as a practical architectural mechanism for mitigating multi-physics interference in universal neural operators.