Introducing VSPINN: A PINN-Based Methodology for High-Dimensional Variation Simulation

Variation Simulation (VS) is a well-established approach for evaluating how input variability propagates through a system, supporting both design improvements and process robustness. It is particularly relevant in applications involving deformable components – such as in assembly processes – where numerical solvers are typically required to capture the underlying physics. These scenarios often involve complex, multi-physics interactions and high-dimensional parametric spaces, making the exhaustive exploration of input configurations computationally demanding. Traditional VS approaches, based on Monte Carlo sampling combined with Finite Element Method (FEM) simulations, quickly become infeasible due to excessive computational cost. This work presents a novel methodology that employs Physics-Informed Neural Networks (PINNs) to perform efficient and real-time Variation Simulation. Unlike standard PINNs, which are typically applied to deterministic or inverse problems, the proposed framework treats variable input parameters as part of the model’s domain. The method integrates automatic loss weighting, residual-based adaptive sampling, and exact boundary condition enforcement to improve accuracy and training stability in high-dimensional spaces. Validation on test cases confirms the method’s effectiveness in mitigating the curse of dimensionality and sets the stage for future applications involving complex multi-physics systems.