Physics informed deep operator networks speed up training for complex problems
The importance of tensor handling and implementation of physics-informed DeepONets
Machine Learning
Summary
Many computer models that predict physical systems need lots of data, which can be expensive or hard to get. The authors work on a special kind of AI called physics-informed DeepONets that use rules from physics to learn with less data. They found that by changing how the AI handles its input data, it trains much faster and uses less memory, especially for complex 3D problems. This makes the AI practical for bigger and harder tasks while keeping accuracy high.
What this means in practice
- •For computational engineers: Train physics-informed DeepONets more efficiently to solve large-scale engineering simulations with lower computational costs and memory demands.
- •For software developers for scientific computing: Implement optimized DeepONet architectures that reduce training time and enable 3D physical problem solving on common GPU hardware.
Authors
Nahum Banks, Gustavo A. M. de Almeida, Sergio Maldonado
Abstract
Physics-informed neural networks (PINNs) reduce or eliminate the need for large labelled datasets by enforcing governing equations during training. Physics-informed Deep Operator Networks (PI-DeepONets) extend this approach to learning solution operators, enabling rapid prediction across families of problems. Despite these advantages, we show that their application to higher-dimensional problems remains limited by the computational cost of training. To address this issue, we propose a modified PI-DeepONet architecture that reduces this cost by removing redundancy in how the Branch network processes input functions across collocation points. The proposed formulation is mathematically equivalent to the original architecture but reduces input tensor sizes and the number of Branch network evaluations. We analyse the computational complexity of both architectures and derive theoretical scaling laws for training time with respect to the number of collocation points and input functions. The proposed architecture is evaluated on 1D, 2D, and 3D linear advection problems. In all cases, it achieves comparable predictive accuracy to the original PI-DeepONet while consistently reducing training time. In 2D experiments, a maximum speed-up of $3.75\times$ is observed, with empirical training-time scaling agreeing with the predicted linear dependence on collocation points and input functions. Furthermore, training a 3D model on an NVIDIA A100 GPU is only feasible using the proposed architecture, as the original formulation exceeds memory limits. These results demonstrate that careful consideration of how PI-DeepONets are implemented can yield substantial gains, enhancing the practical performance of PI-DeepONets and enabling their application to otherwise intractable physics-informed learning problems.