| Abstract: |
| Inverse problems in differential equations are central to many scientific and engineering applications, requiring the estimation of model parameters based on noisy or incomplete observations. Traditional numerical methods for solving these problems are computationally expensive, particularly in Bayesian settings, where likelihood evaluations must be performed repeatedly in high-dimensional parameter spaces. In this talk, we investigate neural networks as surrogates to address these challenges. By incorporating a Laplace Approximation, our method efficiently approximates the forward model and provides uncertainty estimates. Compared to traditional methods, this approach significantly reduces computational costs while maintaining accurate posterior approximations. These findings underscore the potential of neural networks for scalable and reliable solutions to inverse problems in complex systems. |
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