This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration. The key construction consists in a mean-reverting SDE that transforms a high-quality image into a degraded counterpart as a mean state with fixed Gaussian noise. Then, by simulating the corresponding reverse-time SDE, we are able to restore the origin of the low-quality image without relying on any task-specific prior knowledge. Crucially, the proposed mean-reverting SDE has a closed-form solution, allowing us to compute the ground truth time-dependent score and learn it with a neural network. Moreover, we propose a maximum likelihood objective to learn an optimal reverse trajectory that stabilizes the training and improves the restoration results. The experiments show that our proposed method achieves highly competitive performance in quantitative comparisons on image deraining, deblurring, and denoising, setting a new state-of-the-art on two deraining datasets. Finally, the general applicability of our approach is further demonstrated via qualitative results on image super-resolution, inpainting, and dehazing. Code is available at https://github.com/Algolzw/image-restoration-sde.

The convergence of the conjugate gradient method for solving large-scale and sparse linear equation systems depends on the spectral properties of the system matrix, which can be improved by preconditioning. In this paper, we develop a computationally efficient data-driven approach to accelerate the generation of effective preconditioners. We, therefore, replace the typically hand-engineered preconditioners by the output of graph neural networks. Our method generates an incomplete factorization of the matrix and is, therefore, referred to as neural incomplete factorization (NeuralIF). Optimizing the condition number of the linear system directly is computationally infeasible. Instead, we utilize a stochastic approximation of the Frobenius loss which only requires matrix-vector multiplications for efficient training. At the core of our method is a novel message-passing block, inspired by sparse matrix theory, that aligns with the objective of finding a sparse factorization of the matrix. We evaluate our proposed method on both synthetic problem instances and on problems arising from the discretization of the Poisson equation on varying domains. Our experiments show that by using data-driven preconditioners within the conjugate gradient method we are able to speed up the convergence of the iterative procedure. The code is available at https://github.com/paulhausner/neural-incomplete-factorization.

Diffusion policy has shown a strong ability to express complex action distributions in offline reinforcement learning (RL). However, it suffers from overestimating Q-value functions on out-of-distribution (OOD) data points due to the offline dataset limitation. To address it, this paper proposes a novel entropy-regularized diffusion policy and takes into account the confidence of the Q-value prediction with Q-ensembles. At the core of our diffusion policy is a mean-reverting stochastic differential equation (SDE) that transfers the action distribution into a standard Gaussian form and then samples actions conditioned on the environment state with a corresponding reverse-time process. We show that the entropy of such a policy is tractable and that can be used to increase the exploration of OOD samples in offline RL training. Moreover, we propose using the lower confidence bound of Q-ensembles for pessimistic Q-value function estimation. The proposed approach demonstrates state-of-the-art performance across a range of tasks in the D4RL benchmarks, significantly improving upon existing diffusion-based policies. The code is available at https://github. com/ruoqizzz/entropy-offlineRL.

The integration of automation and data-driven methodologies offers a promising approach to accelerating materials discovery in energy storage research. Thus far, in battery research, coin-cell assembly has advanced to become nearly fully automated but remains largely disconnected from data-driven methods. To bridge the disconnect, this work presents a self-driving laboratory framework to accelerate electrolyte discovery by integrating automated coin-cell assembly, galvanostatic cycling of LiFePO4||Li4Ti5O12 organic-aqueous full cells, and Bayesian optimization for selecting subsequent experiments based on prior results. The study explored an organic-aqueous hybrid electrolyte system comprising four co-solvents and two lithium-conducting salts. Using this framework, cells with an optimized electrolyte cycled with at least 94% Coulombic efficiency. Additionally, online electrochemical mass spectrometry …

Metal anodes provide the highest energy density in batteries. However, they still suffer from electrode/electrolyte interface side reactions and dendrite growth, especially under fast-charging conditions. In this paper, we consider a phase-field model of electrodeposition in metal-anode batteries and provide a scalable, versatile framework for optimizing its chemical parameters. Our approach is based on Bayesian optimization and explores the parameter space with a high sample efficiency and a low computation complexity. We use this framework to find the optimal cell for suppressing dendrite growth and accelerating charging speed under constant voltage. We identify interfacial mobility as a key parameter, which should be maximized to inhibit dendrites without compromising the charging speed. The results are verified using extended simulations of dendrite evolution in charging half cells with lithium-metal anodes.