Tracking large chemical reaction networks and rare events by neural networks

Researchers have introduced a robust strategy for physics-informed neural networks (PINNs) that incorporates hidden physical laws as soft constraints during training. This approach addresses the challenge of ensuring that neural networks accurately reflect the physical structures embedded in partial differential equations, particularly for irreversible processes. The method enhances the reliability of solutions across various scientific benchmarks, including wave propagation and combustion.

A new numerical method has been proposed to approximate solution operators derived from Backward Stochastic Differential Equations (BSDEs), utilizing Wiener chaos decomposition and the classical Euler scheme. This method demonstrates convergence under mild assumptions and is implemented using neural networks, with numerical examples validating its accuracy.

The empirical evaluation of Frank-Wolfe methods for constructing white-box adversarial attacks highlights the need for efficient adversarial attack construction in neural networks, particularly focusing on numerical optimization techniques. The study emphasizes the application of modified Frank-Wolfe methods to enhance the robustness of neural networks against adversarial threats, utilizing datasets like MNIST and CIFAR-10 for testing.

The Parallel Trust Assessment System (PaTAS) has been introduced as a framework for modeling and propagating trust in neural networks using Subjective Logic. This framework aims to address the inadequacies of traditional evaluation metrics in capturing uncertainty and reliability in AI predictions, particularly in critical applications.