Adaptive Mesh-based Scalable Learned Simulation and Optimization of Manufacturing Processes

• Applicants: Professorin Dr.-Ing. Luise Kärger; Professor Dr. Gerhard Neumann
• Subject Area: Methods in Artificial Intelligence and Machine Learning
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 570157846

We aim to advance the efficiency and applicability of Machine Learning (ML)-based physics simulators for simulating complex engineering tasks. Traditionally, engineering optimization has relied on costly trial-and-error experiments and, more recently, on physics-based simulations made possible by increased computing power. These simulations, grounded in physical principles and described by partial differential equations, are crucial for reducing prototyping costs and time. However, their high computational demands still limit their use in extensive parameter studies and optimization tasks. ML-based approaches show promise by offering substantial speed-ups without sacrificing accuracy, but they require further refinement to address real-world engineering challenges. This project focuses on developing robust and efficient ML methods capable of accurately simulating and optimizing complex engineering problems. We target representative applications in Thermochemical Curing (TC), Injection Molding (IM), and Additive Manufacturing (AM), all of which present significant modeling challenges. We aim to develop efficient algorithms for learning to simulate complex multi-physics problems. This includes designing equivariant architectures for Graph Network Simulators (GNS) that respect material symmetries and extending them with diffusion-based training to improve long-term prediction accuracy. Additionally, we adapt these diffusion-based, material-equivariant models to hierarchical mesh structures to better capture long-range dependencies, and we integrate learned adaptive mesh refinement algorithms to manage computational resources more effectively for large-scale problems. We also develop procedures for scaling data-driven models—trained on small examples—to large engineering parts during inference, enabling cost-effective training while supporting realistic downstream applications. To ensure reliability in optimization, we augment these learned simulators with uncertainty estimation methods, allowing for robust use with black-box optimizers. We address optimization problems that are computationally infeasible with traditional simulations, such as identifying optimal inlet positions in IM or minimizing warpage and residual stress in AM nozzle trajectories. An active learning framework further enhances our models by improving the accuracy and reliability of the optimization objectives. Our approaches will be evaluated using newly created datasets of real-world complexity, which we will publish, as well as on established benchmarks. We will compare performance with both current state-of-the-art learned simulators and classical methods. Where traditional simulations are impractical, we will validate our models using experimental data. Overall, the advancements from this project are expected to enable scalable and practical ML-based simulation and optimization across a wide range of engineering domains.

• DFG Programme: Research Grants