Lukas Fesser

Lukas Fesser, Luca D'Amico-Wong, Richard Qiu

Physics-informed Neural Networks (PINNs) have recently gained popularity due to their effective approximation of partial differential equations (PDEs) using deep neural networks (DNNs). However, their out of domain behavior is not well understood, with previous work speculating that the presence of high frequency components in the solution function might be to blame for poor extrapolation performance. In this paper, we study the extrapolation behavior of PINNs on a representative set of PDEs of different types, including high-dimensional PDEs. We find that failure to extrapolate is not caused by high frequencies in the solution function, but rather by shifts in the support of the Fourier spectrum over time. We term these spectral shifts and quantify them by introducing a Weighted Wasserstein-Fourier distance (WWF). We show that the WWF can be used to predict PINN extrapolation performance, and that in the absence of significant spectral shifts, PINN predictions stay close to the true solution even in extrapolation. Finally, we propose a transfer learning-based strategy to mitigate the effects of larger spectral shifts, which decreases extrapolation errors by up to 82%.

Daqian Shao, Lukas Fesser, Marta Kwiatkowska

Robustness certification, which aims to formally certify the predictions of neural networks against adversarial inputs, has become an integral part of important tool for safety-critical applications. Despite considerable progress, existing certification methods are limited to elementary architectures, such as convolutional networks, recurrent networks and recently Transformers, on benchmark datasets such as MNIST. In this paper, we focus on the robustness certification of scene text recognition (STR), which is a complex and extensively deployed image-based sequence prediction problem. We tackle three types of STR model architectures, including the standard STR pipelines and the Vision Transformer. We propose STR-Cert, the first certification method for STR models, by significantly extending the DeepPoly polyhedral verification framework via deriving novel polyhedral bounds and algorithms for key STR model components. Finally, we certify and compare STR models on six datasets, demonstrating the efficiency and scalability of robustness certification, particularly for the Vision Transformer.