arXiv:2606.12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative. Their relative performance remains difficult to assess because the two approaches are often compared under different formulations, parameterizations, optimizers, and regularization choices. We present a fair comparison of adjoint optimization and PINNs for PDE-constrained inverse problems. From a comm
The rapid advancement of AI, particularly neural networks, is forcing a re-evaluation of traditional computational methods in scientific and engineering fields.
Improving the efficiency and accuracy of solving PDE-constrained inverse problems has direct implications for sectors relying on complex simulations and modeling, from materials science to climate prediction.
This research provides a more rigorous comparison framework for two dominant approaches (adjoint methods vs. PINNs), which can guide future development and deployment strategies for AI in scientific computing.
- · Computational scientists
- · AI researchers specializing in scientific machine learning
- · Engineering simulation software providers
- · Developers of less efficient, niche optimization algorithms
More informed decisions on whether to adopt PINNs or refine adjoint methods for specific PDE inverse problems will be made.
This could accelerate the integration of AI-driven solutions into various scientific and industrial simulation pipelines, leading to faster research cycles and product development.
Long-term, optimized computational methods could enable breakthroughs in areas currently limited by numerical complexity, such as novel material discovery or climate modeling with higher resolution.
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Read at arXiv cs.LG