More Like this

1. Quantum DeepONet: Neural operators accelerated by quantum computing

   https://doi.org/10.22331/q-2025-06-04-1761  

   Xiao, Pengpeng; Zheng, Muqing; Jiao, Anran; Yang, Xiu; Lu, Lu (June 2025, Quantum)

   In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as deep operator network (DeepONet), which learn mappings between infinite-dimensional function spaces, promise efficient computation of PDE solutions for a new condition in a single forward pass. However, classical DeepONet entails quadratic complexity concerning input dimensions during evaluation. Given the progress in quantum algorithms and hardware, here we propose to utilize quantum computing to accelerate DeepONet evaluations, yielding complexity that is linear in input dimensions. Our proposed quantum DeepONet integrates unary encoding and orthogonal quantum layers. We benchmark our quantum DeepONet using a variety of PDEs, including the antiderivative operator, advection equation, and Burgers' equation. We demonstrate the method's efficacy in both ideal and noisy conditions. Furthermore, we show that our quantum DeepONet can also be informed by physics, minimizing its reliance on extensive data collection. Quantum DeepONet will be particularly advantageous in applications in outer loop problems which require exploring parameter space and solving the corresponding PDEs, such as uncertainty quantification and optimal experimental design. 

   more » « less
2. A Causality-DeepONet for Causal Responses of Linear Dynamical Systems

   https://doi.org/10.4208/cicp.OA-2023-0078  

   Liu, Lizuo; null, Kamaljyoti Nath; Cai, Wei (May 2024, Communications in Computational Physics)
3. Fed-DeepONet: Stochastic Gradient-Based Federated Training of Deep Operator Networks

   https://doi.org/10.3390/a15090325  

   Moya, Christian; Lin, Guang (September 2022, Algorithms)

   The Deep Operator Network (DeepONet) framework is a different class of neural network architecture that one trains to learn nonlinear operators, i.e., mappings between infinite-dimensional spaces. Traditionally, DeepONets are trained using a centralized strategy that requires transferring the training data to a centralized location. Such a strategy, however, limits our ability to secure data privacy or use high-performance distributed/parallel computing platforms. To alleviate such limitations, in this paper, we study the federated training of DeepONets for the first time. That is, we develop a framework, which we refer to as Fed-DeepONet, that allows multiple clients to train DeepONets collaboratively under the coordination of a centralized server. To achieve Fed-DeepONets, we propose an efficient stochastic gradient-based algorithm that enables the distributed optimization of the DeepONet parameters by averaging first-order estimates of the DeepONet loss gradient. Then, to accelerate the training convergence of Fed-DeepONets, we propose a moment-enhanced (i.e., adaptive) stochastic gradient-based strategy. Finally, we verify the performance of Fed-DeepONet by learning, for different configurations of the number of clients and fractions of available clients, (i) the solution operator of a gravity pendulum and (ii) the dynamic response of a parametric library of pendulums. 

   more » « less
4. Transfer learning enhanced DeepONet for long-time prediction of evolution equation

   Xu, Wuzhe; Lu, Yulong; Wang, Li (January 2023, Proceedings of the AAAI Conference on Artificial Intelligence)

   Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it pro- vides an efficient approach to predict the evolution equations in a finite time horizon. Nevertheless, the vanilla DeepONet suffers from the issue of stability degradation in the long- time prediction. This paper proposes a transfer-learning aided DeepONet to enhance the stability. Our idea is to use transfer learning to sequentially update the DeepONets as the surro- gates for propagators learned in different time frames. The evolving DeepONets can better track the varying complexities of the evolution equations, while only need to be updated by efficient training of a tiny fraction of the operator networks. Through systematic experiments, we show that the proposed method not only improves the long-time accuracy of Deep- ONet while maintaining similar computational cost but also substantially reduces the sample size of the training set. 

   more » « less
5. A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

   https://doi.org/10.1016/j.cma.2022.114587  

   Goswami, Somdatta; Yin, Minglang; Yu, Yue; Karniadakis, George Em (March 2022, Computer Methods in Applied Mechanics and Engineering)