This study introduces a modified score matching method aimed at generating molecular structures with high energy accuracy. The denoising process of score matching or diffusion models mirrors molecular structure optimization, where scores act like physical force fields that guide particles toward equilibrium states. To achieve energetically accurate structures, it can be advantageous to have the score closely approximate the gradient of the actual potential energy surface. Unlike conventional methods that simply design the target score based on structural differences in Euclidean space, we propose a Riemannian score matching approach. This method represents molecular structures on a manifold defined by physics-informed internal coordinates to efficiently mimic the energy landscape, and performs noising and denoising within this space. Our method has been evaluated by refining several types of starting structures on the QM9 and GEOM datasets, demonstrating that the proposed Riemannian score matching method significantly improves the accuracy of the generated molecular structures, attaining chemical accuracy. The implications of this study extend to various applications in computational chemistry, offering a robust tool for accurate molecular structure prediction.

The popularity of mobile vision creates a demand for advanced compact computational imaging systems, which call for the development of both a lightweight optical system and an effective image reconstruction model. Recently, joint design pipelines come to the research forefront, where the two significant components are simultaneously optimized via data-driven learning to realize the optimal system design. However, the effectiveness of these designs largely depends on the initial setup of the optical system, complicated by a non-convex solution space that impedes reaching a globally optimal solution. In this work, we present Global Search Optics (GSO) to automatically design compact computational imaging systems through two parts: (i) Fused Optimization Method for Automatic Optical Design (OptiFusion), which searches for diverse initial optical systems under certain design specifications; and (ii) Efficient Physic-aware Joint Optimization (EPJO), which conducts parallel joint optimization of initial optical systems and image reconstruction networks with the consideration of physical constraints, culminating in the selection of the optimal solution. Extensive experimental results on the design of three-piece (3P) sphere computational imaging systems illustrate that the GSO serves as a transformative end-to-end lens design paradigm for superior global optimal structure searching ability, which provides compact computational imaging systems with higher imaging quality compared to traditional methods. The source code will be made publicly available at https://github.com/wumengshenyou/GSO.

Graph neural networks (GNNs) have drawn more and more attention from material scientists and demonstrated a high capacity to establish connections between the structure and properties. However, with only unrelaxed structures provided as input, few GNN models can predict the thermodynamic properties of relaxed configurations with an acceptable level of error. In this work, we develop a multi-task (MT) architecture based on DimeNet++ and mixture density networks to improve the performance of such task. Taking CO adsorption on Cu-based single-atom alloy catalysts as an illustration, we show that our method can reliably estimate CO adsorption energy with a mean absolute error of 0.087 eV from the initial CO adsorption structures without costly first-principles calculations. Further, compared to other state-of-the-art GNN methods, our model exhibits improved generalization ability when predicting catalytic performance of out-of-domain configurations, built with either unseen substrate surfaces or doping species. We show that the proposed MT GNN strategy can facilitate catalyst discovery.

Layout design with complex constraints is a challenging problem to solve due to the non-uniqueness of the solution and the difficulties in incorporating the constraints into the conventional optimization-based methods. In this paper, we propose a design method based on the recently developed machine learning technique, Variational Autoencoder (VAE). We utilize the learning capability of the VAE to learn the constraints and the generative capability of the VAE to generate design candidates that automatically satisfy all the constraints. As such, no constraints need to be imposed during the design stage. In addition, we show that the VAE network is also capable of learning the underlying physics of the design problem, leading to an efficient design tool that does not need any physical simulation once the network is constructed. We demonstrated the performance of the method on two cases: inverse design of surface diffusion induced morphology change and mask design for optical microlithography.