Physics-informed neural networks (PINNs) have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant challenges remain—particularly regarding training stability and the lack of rigorous theoretical guarantees, especially when compared to classical...
Advanced adaptive optics (AO) instruments use Fourier-type wavefront sensors (WFSs) to measure and correct wavefront distortions caused by the Earth's atmosphere. Conventionally, the wavefront reconstruction relies on matrix-vector-multiplications (MVMs). However, these linear estimators assume small wavefront aberrations and may fail to capture the nonlinear behavior of Fourier-type wavefront...
In this talk we study the minimization of convex, $L$-smooth functions defined on a separable real Hilbert space. We analyze regularized stochastic gradient descent (reg-SGD), a variant of stochastic gradient descent that uses a Tikhonov regularization with time-dependent, vanishing regularization parameter. We prove strong convergence of reg-SGD to the minimum-norm solution of the original...
