Compositional Meta-Learning for Mitigating Task Heterogeneity in Physics-Informed Neural Networks

arXiv cs.AI / 5/1/2026

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Key Points

The paper proposes LAM-PINN, a compositional meta-learning framework for physics-informed neural networks (PINNs) to better handle heterogeneous tasks in parameterized PDE families.
Instead of using a single global initialization, LAM-PINN builds task representations using PDE parameters plus learning-affinity metrics from brief transfer sessions, enabling task clustering even when inputs are coordinate-only.
The approach decomposes the model into cluster-specialized subnetworks and a shared meta network, learning routing weights to reuse the most relevant modules and avoid negative transfer.
Experiments on three PDE benchmarks show an average 19.7× reduction in MSE on unseen tasks while using only 10% of the training iterations compared with conventional PINNs.
Overall, the results suggest LAM-PINN can generalize effectively to unseen PDE configurations within bounded design spaces, making it promising for resource-constrained engineering workflows.

Abstract

Physics-informed neural networks (PINNs) approximate solutions of partial differential equations (PDEs) by embedding physical laws into the loss function. In parameterized PDE families, variations in coefficients or boundary/initial conditions define distinct tasks. This makes training individual PINNs for each task computationally prohibitive, while cross-task transfer can be sensitive to task heterogeneity. While meta-learning can reduce retraining cost, existing methods often rely on a single global initialization and may suffer from negative transfer, particularly under feature-scarce coordinate inputs and limited training-task availability. We propose the Learning-Affinity Adaptive Modular Physics-Informed Neural Network (LAM-PINN), a compositional framework that leverages task-specific learning dynamics. LAM-PINN combines PDE parameters with learning-affinity metrics from brief transfer sessions to construct a task representation and cluster tasks even with coordinate-only inputs. It decomposes the model into cluster-specialized subnetworks and a shared meta network, and learns routing weights to selectively reuse modules instead of relying on a single global initialization. Across three PDE benchmarks, LAM-PINN achieves an average 19.7-fold reduction in mean squared error (MSE) on unseen tasks using only 10% of the training iterations required by conventional PINNs. These results indicate its effectiveness for generalization to unseen configurations within bounded design spaces of parameterized PDE families in resource-constrained engineering settings.