Haihui Ruan

Wei Wang, Maryam Hakimzadeh, Haihui Ruan et al.

Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way to accelerate simulations, but their practical deployment is hindered by several challenges: they typically require large volumes of training data generated from high-fidelity solvers, tend to accumulate errors over time in dynamical settings, and often exhibit poor generalization in multiphysics scenarios. This work introduces a novel hybrid framework that integrates physics-informed deep operator network with FEM through domain decomposition and leverages numerical analysis for time marching. Our innovation lies in efficient coupling FE and DeepONet subdomains via a Schwarz method, expecting to solve complex and nonlinear regions by a pretrained DeepONet, while the remainder is handled by conventional FE. To address the challenges of dynamic systems, we embed a time stepping scheme directly into the DeepONet, substantially reducing long-term error propagation. Furthermore, an adaptive subdomain evolution strategy enables the ML-resolved region to expand dynamically, capturing fine-scale features without remeshing. Our framework shows accelerated convergence rates (up to 20% improvement in convergence rates compared to conventional FE coupling approaches) while preserving solution fidelity with error margins consistently below 3%. Our study shows that our proposed hybrid solver: (1) reduces computational costs by eliminating fine mesh requirements, (2) mitigates error accumulation in time-dependent simulations, and (3) enables automatic adaptation to evolving physical phenomena. This work establishes a new paradigm for coupling state of the art physics based and machine learning solvers in a unified framework, offering a robust, reliable, and scalable pathway for high fidelity multiscale simulations.

Yuzhou Zhang, Mohan Hua, Jinan Liu et al.

Many glass products require thermoformed geometry with high precision. However, the traditional approach of developing a thermoforming process through trials and errors can cause large waste of time and resources and often end up with unsuccessfulness. Hence, there is a need to develop an efficient predictive model, replacing the costly simulations or experiments, to assist the design of precision glass thermoforming. In this work, we report a surrogate model, based on a dimensionless back-propagation neural network (BPNN), that can adequately predict the form errors and thus compensate for these errors in mold design using geometric features and process parameters as inputs. Our trials with simulation and industrial data indicate that the surrogate model can predict forming errors with adequate accuracy. Although perception errors (mold designers' decisions) and mold fabrication errors make the industrial training data less reliable than simulation data, our preliminary training and testing results still achieved a reasonable consistency with industrial data, suggesting that the surrogate models are directly implementable in the glass-manufacturing industry.