On the Convergence of Locally Adaptive and Scalable Diffusion-Based Sampling Methods for Deep Bayesian Neural Network Posteriors

Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural network's prediction. Bayesian neural networks are a promising approach for modeling uncertainties in deep neural networks. Unfortunately, generating samples from the posterior distribution of neural networks is a major challenge. One significant advance in that direction would be the incorporation of adaptive step sizes, similar to modern neural network optimizers, into Monte Carlo Markov chain sampling algorithms without significantly increasing computational demand. Over the past years, several papers have introduced sampling algorithms with claims that they achieve this property. However, do they indeed converge to the correct distribution? In this paper, we demonstrate that these methods can have a substantial bias in the distribution they sample, even in the limit of vanishing step sizes and at full batch size.

Position Paper on Materials Design -- A Modern Approach

Traditional design cycles for new materials and assemblies have two fundamental drawbacks. The underlying physical relationships are often too complex to be precisely calculated and described. Aside from that, many unknown uncertainties, such as exact manufacturing parameters or materials composition, dominate the real assembly behavior. Machine learning (ML) methods overcome these fundamental limitations through data-driven learning. In addition, modern approaches can specifically increase system knowledge. Representation Learning allows the physical, and if necessary, even symbolic interpretation of the learned solution. In this way, the most complex physical relationships can be considered and quickly described. Furthermore, generative ML approaches can synthesize possible morphologies of the materials based on defined conditions to visualize the effects of uncertainties. This modern approach accelerates the design process for new materials and enables the prediction and interpretation of realistic materials behavior.

High Accuracy Uncertainty-Aware Interatomic Force Modeling with Equivariant Bayesian Neural Networks

Even though Bayesian neural networks offer a promising framework for modeling uncertainty, active learning and incorporating prior physical knowledge, few applications of them can be found in the context of interatomic force modeling. One of the main challenges in their application to learning interatomic forces is the lack of suitable Monte Carlo Markov chain sampling algorithms for the posterior density, as the commonly used algorithms do not converge in a practical amount of time for many of the state-of-the-art architectures. As a response to this challenge, we introduce a new Monte Carlo Markov chain sampling algorithm in this paper which can circumvent the problems of the existing sampling methods. In addition, we introduce a new stochastic neural network model based on the NequIP architecture and demonstrate that, when combined with our novel sampling algorithm, we obtain predictions with state-of-the-art accuracy as well as a good measure of uncertainty.