Physics simulations in milliseconds

Simulations: The foundation of modern research and technology

Physical simulations are of central importance in many engineering and natural sciences, as they make it possible to precisely model the behavior of complex systems. Particularly noteworthy is the finite element method (FEM), a proven numerical technique for solving partial differential equations that is widely used in fields such as structural mechanics, fluid mechanics and electromagnetism. Despite their high accuracy, however, these simulations are often computationally intensive and involve long calculation times. This is precisely where artificial intelligence (AI) can come in: It offers the potential to significantly speed up physical simulations without significantly compromising accuracy.

Artificial intelligence as a performance booster

The promising deep surrogate approach is based on training a deep neural network as a substitute model for a numerical simulation method [1]. The network is first trained with a large, representative amount of simulation data that was previously generated using precise but time-consuming FEM simulators. Once the training is complete, the neural network is able to deliver the simulation results for any input data in milliseconds instead of seconds or minutes with a numerical solution method. The particular advantage of surrogate models is that the network only needs to be trained once in advance. In subsequent use, simulation results can be calculated in real time and with high precision, which, for example, enables considerable increases in efficiency for simulation-based design optimizations of aerodynamic components or electrical circuits.

Figure 1: Schematic of a replacement model including creation and application phase

Application in the FFG project nARvibrain

We were able to successfully implement a concrete application of the surrogate model approach in the FFG project nARvibrain. The project is being carried out in collaboration with the Medical University of Graz, Cortexplore GmbH and FH JOANNEUM and uses transcranial magnetic stimulation (TMS) to localize important functional brain areas of a tumour patient preoperatively. This serves as important information for the surgeon in the subsequent tumor removal [2]. In the TMS application, a coil is held to the patient’s head in order to generate electrical currents in the brain that specifically suppress or stimulate certain brain functions. The precise positioning and alignment of the coil on the head are crucial for the effectiveness of the treatment. Physical simulations of the currents induced in the brain by TMS can be used to determine the optimal coil positioning.

As part of nARvibrain, a surrogate model was developed that predicts the optimal coil positioning for a specific target area in the brain in real time.

This information is to be displayed directly to the doctor via an augmented reality system and support them in manual coil guidance. This technology is intended to make TMS treatment more individual, efficient and effective. The replacement model approach for optimizing TMS coil positioning was published in the renowned journal Nature Scientific Reports [3].

Figure 2: (left) Schematic sequence of a TMS treatment, (right) comparison of the predictions of the equivalent model-based coil optimization and the FEM-based reference optimization from Ref. [3].

References

[1] Pestourie, R., et al. Physics-enhanced deep surrogates for partial differential equations. Nat Mach Intell 5, 1458-1465 (2023). https://doi.org/10.1038/s42256-023-00761-y
[2] https://www.risc-software.at/referenzprojekte/narvibrain/
[3] Moser, P., et al. Real-time estimation of the optimal coil placement in transcranial magnetic stimulation using multi-task deep learning. Sci Rep 14, 19361 (2024). https://doi.org/10.1038/s41598-024-70367-w