Uncertainty Quantification for Physics-Informed Neural Networks with Extended Fiducial Inference

Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a prominent model in scientific machine learning, uncertainty is typically quantified using Bayesian or dropout methods. However, both approaches suffer from a fundamental limitation: the prior distribution or dropout rate required to construct honest confidence sets cannot be determined without additional information. In this paper, we propose a novel method within the framework of extended fiducial inference (EFI) to provide rigorous uncertainty quantification for PINNs. The proposed method leverages a narrow-neck hyper-network to learn the parameters of the PINN and quantify their uncertainty based on imputed random errors in the observations. This approach overcomes the limitations of Bayesian and dropout methods, enabling the construction of honest confidence sets based solely on observed data. This advancement represents a significant breakthrough for PINNs, greatly enhancing their reliability, interpretability, and applicability to real-world scientific and engineering challenges. Moreover, it establishes a new theoretical framework for EFI, extending its application to large-scale models, eliminating the need for sparse hyper-networks, and significantly improving the automaticity and robustness of statistical inference.

FSD: An Initial Chinese Dataset for Fake Song Detection

Singing voice synthesis and singing voice conversion have significantly advanced, revolutionizing musical experiences. However, the rise of "Deepfake Songs" generated by these technologies raises concerns about authenticity. Unlike Audio DeepFake Detection (ADD), the field of song deepfake detection lacks specialized datasets or methods for song authenticity verification. In this paper, we initially construct a Chinese Fake Song Detection (FSD) dataset to investigate the field of song deepfake detection. The fake songs in the FSD dataset are generated by five state-of-the-art singing voice synthesis and singing voice conversion methods. Our initial experiments on FSD revealed the ineffectiveness of existing speech-trained ADD models for the task of song deepFake detection. Thus, we employ the FSD dataset for the training of ADD models. We subsequently evaluate these models under two scenarios: one with the original songs and another with separated vocal tracks. Experiment results show that song-trained ADD models exhibit a 38.58% reduction in average equal error rate compared to speech-trained ADD models on the FSD test set.