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

• URL: http://arxiv.org/abs/2604.26999v1
• Date: Wed, 29 Apr 2026 03:09:57 GMT
• Title: Compositional Meta-Learning for Mitigating Task Heterogeneity in Physics-Informed Neural Networks
• Abstract summary: Physics-informed neural networks (PINNs) approximate solutions of partial differential equations (PDEs) by embedding physical laws into the loss function.<n>LAM-PINN combines PDE parameters with learning-affinity metrics to construct a task representation and cluster tasks even with coordinate-only inputs.<n>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.
• Score: 44.4483539967295
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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