Integrating graph neural networks (GNNs) with variational inference (VI) provides a promising direction for blending structured prior knowledge with observational empirical data for data-driven industrial process modeling. However, this task requires inference of the normalized adjacency matrix (NAM), where each row is normalized to be non-negative and to sum to one, matching the support of Dirichlet distribution. This requirement presents two main technical challenges: 1) intractable Kullback-Leibler (KL) divergence optimization between Dirichlet distributions, and 2) constrained optimization for standard- gradient-descent-based neural network parameter optimization. To handle issue 1), we first formulate the inference of the NAM as a differential equation simulation problem and derive an easy-to-implement expression to iteratively improve the KL divergence without explicitly computing it. Based on this, to alleviate issue 2), we involve Riemannian optimization to precondition this simulation procedure, which ensures that the inferred NAM conforms to the row-normalization constraint. After that, we collectively designate these approaches for NAM inference as Preconditioned-Simulation-Induced Variational Inference ($\psi$-VI), and provide theoretical guarantees of convergence. On this foundation, we propose a new graph neural network architecture, the Preconditioned-Simulation-Induced-based Variational Graph Neural Network ($\psi$-VGNN) for industrial process modeling. Finally, we validate the efficacy of$\psi$-VGNN through comprehensive experiments on industrial modeling tasks.

Motif-scaffolding is a fundamental component of protein design, which aims to construct the scaffold structure that stabilizes motifs conferring desired functions. Recent advances in generative models are promising for designing scaffolds, with two main approaches: training-based and sampling-based methods. Training-based methods are resource-heavy and slow, while training-free sampling-based methods are flexible but require numerous sampling steps and costly, unstable guidance. To speed up and improve sampling-based methods, we analyzed failure cases and found that errors stem from the trade-off between generation and guidance. Thus we proposed to exploit the spatial context and adjust the generative direction to be consistent with guidance to overcome this trade-off. Motivated by this, we formulate motif-scaffolding as a Geometric Inverse Design task inspired by the image inverse problem, and present Evolution-ViA-reconstruction (EVA), a novel sampling-based coupled flow framework on geometric manifolds, which starts with a pretrained flow-based generative model. EVA uses motif-coupled priors to leverage spatial contexts, guiding the generative process along a straighter probability path, with generative directions aligned with guidance in the early sampling steps. EVA is 70× faster than SOTA model RFDiffusion with competitive and even better performance on benchmark tests. Further experiments on real-world cases including vaccine design, multi-motif scaffolding and motif optimal placement searching demonstrate EVA's superior efficiency and effectiveness.

Structure-based drug design (SBDD) aims to generate potential drugs that can bind to a target protein and is greatly expedited by the aid of AI techniques in generative models. However, a lack of systematic understanding persists due to the diverse settings, complex implementation, difficult reproducibility, and task singularity. Firstly, the absence of standardization can lead to unfair comparisons and inconclusive insights. To address this dilemma, we propose CBGBench, a comprehensive benchmark for SBDD, that unifies the task as a generative graph completion, analogous to fill-in-the-blank of the 3D complex binding graph. By categorizing existing methods based on their attributes, CBGBench facilitates a modular and extensible framework that implements cutting-edge methods. Secondly, a single de novo molecule generation task can hardly reflect their capabilities. To broaden the scope, we adapt these models to a range of tasks essential in drug design, considered sub-tasks within the graph fill-in-the-blank tasks. These tasks include the generative designation of de novo molecules, linkers, fragments, scaffolds, and sidechains, all conditioned on the structures of protein pockets. Our evaluations are conducted with fairness, encompassing comprehensive perspectives on interaction, chemical properties, geometry authenticity, and substructure validity. We further provide insights with analysis from empirical studies. Our results indicate that there is potential for further improvements on many tasks, with optimization in network architectures, and effective incorporation of chemical prior knowledge. Finally, to lower the barrier to entry and facilitate further developments in the field, we also provide a single [codebase](https://github.com/EDAPINENUT/CBGBench) that unifies the discussed models, data pre-processing, training, sampling, and evaluation.

Protein structure-based property prediction has emerged as a promising approach for various biological tasks, such as protein function prediction and sub-cellular location estimation. The existing methods highly rely on experimental protein structure data and fail in scenarios where these data are unavailable. Predicted protein structures from AI tools (e.g., AlphaFold2) were utilized as alternatives. However, we observed that current practices, which simply employ accurately predicted structures during inference, suffer from notable degradation in prediction accuracy. While similar phenomena have been extensively studied in general fields (e.g., Computer Vision) as model robustness, their impact on protein property prediction remains unexplored. In this paper, we first investigate the reason behind the performance decrease when utilizing predicted structures, attributing it to the structure embedding bias from the perspective of structure representation learning. To study this problem, we identify a Protein 3D Graph Structure Learning Problem for Robust Protein Property Prediction (PGSL-RP3), collect benchmark datasets, and present a protein Structure embedding Alignment Optimization framework (SAO) to mitigate the problem of structure embedding bias between the predicted and experimental protein structures. Extensive experiments have shown that our framework is model-agnostic and effective in improving the property prediction of both predicted structures and experimental structures.

Accurate prediction of protein-ligand binding structures, a task known as molecular docking is crucial for drug design but remains challenging. While deep learning has shown promise, existing methods often depend on holo-protein structures (docked, and not accessible in realistic tasks) or neglect pocket sidechain conformations, leading to limited practical utility and unrealistic conformation predictions. To fill these gaps, we introduce an under-explored task, named flexible docking to predict poses of ligand and pocket sidechains simultaneously and introduce Re-Dock, a novel diffusion bridge generative model extended to geometric manifolds. Specifically, we propose energy-to-geometry mapping inspired by the Newton-Euler equation to co-model the binding energy and conformations for reflecting the energy-constrained docking generative process. Comprehensive experiments on designed benchmark datasets including apo-dock and cross-dock demonstrate our model's superior effectiveness and efficiency over current methods.

Increasing works for antibody design are emerging to generate sequences and structures in Complementarity Determining Regions (CDRs), but problems still exist. We focus on two of them: (i) authenticity of the generated structure and (ii) rationality of the affinity maturation, and propose GeoAB as a solution. In specific, GeoAB-Designergenerates CDR structures with realistic internal geometries, composed of a generative geometry initializer (Geo-Initializer) and a position refiner (Geo-Refiner); GeoAB-Optimizer achieves affinity maturation by accurately predicting both the mutation effects and structures of mutant antibodies with the same network architecture as Geo-Refiner. Experiments show that GeoAB achieves state-of-the-art performance in CDR co-design and mutation effect predictions, and fulfills the discussed tasks effectively.

Therapeutic peptides have proven to have great pharmaceutical value and potential in recent decades. However, methods of AI-assisted peptide drug discovery are not fully explored. To fill the gap, we propose a target-aware peptide design method called PPFlow, based on conditional flow matching on torus manifolds, to model the internal geometries of torsion angles for the peptide structure design. Besides, we establish a protein-peptide binding dataset named PPBench2024 to fill the void of massive data for the task of structure-based peptide drug design and to allow the training of deep learning methods. Extensive experiments show that PPFlow reaches state-of-the-art performance in tasks of peptide drug generation and optimization in comparison with baseline models, and can be generalized to other tasks including docking and side-chain packing.

Diffusion models have demonstrated competitive performance in missing data imputation (MDI) task. However, directly applying diffusion models to MDI produces suboptimal performance due to two primary defects. First, the sample diversity promoted by diffusion models hinders the accurate inference of missing values. Second, data masking reduces observable indices for model training, obstructing imputation performance. To address these challenges, we introduce $\underline{\text{N}}$egative $\underline{\text{E}}$ntropy-regularized $\underline{\text{W}}$asserstein gradient flow for $\underline{\text{Imp}}$utation (NewImp), enhancing diffusion models for MDI from a gradient flow perspective. To handle the first defect, we incorporate a negative entropy regularization term into the cost functional to suppress diversity and improve accuracy. To handle the second defect, we demonstrate that the imputation procedure of NewImp, induced by the conditional distribution-related cost functional, can equivalently be replaced by that induced by the joint distribution, thereby naturally eliminating the need for data masking. Extensive experiments validate the effectiveness of our method. Code is available at [https://github.com/JustusvLiebig/NewImp](https://github.com/JustusvLiebig/NewImp).

Protein loops play a critical role in the dynamics of proteins and are essential for numerous biological functions, and various computational approaches to loop modeling have been proposed over the past decades. However, a comprehensive understanding of the strengths and weaknesses of each method is lacking. In this work, we constructed two high-quality datasets (i.e. the General dataset and the CASP dataset) and systematically evaluated the accuracy and efficiency of 13 commonly used loop modeling approaches from the perspective of loop lengths, protein classes and residue types. The results indicate that the knowledge-based method FREAD generally outperforms the other tested programs in most cases, but encountered challenges when predicting loops longer than 15 and 30 residues on the CASP and General datasets, respectively. The ab initio method Rosetta NGK demonstrated exceptional modeling accuracy for short loops with four to eight residues and achieved the highest success rate on the CASP dataset. The well-known AlphaFold2 and RoseTTAFold require more resources for better performance, but they exhibit promise for predicting loops longer than 16 and 30 residues in the CASP and General datasets. These observations can provide valuable insights for selecting suitable methods for specific loop modeling tasks and contribute to future advancements in the field.

In recent years, AI-assisted drug design methods have been proposed to generate molecules given the pockets' structures of target proteins. Most of them are {\em atom-level-based} methods, which consider atoms as basic components and generate atom positions and types. In this way, however, it is hard to generate realistic fragments with complicated structures. To solve this, we propose \textsc{D3FG}, a {\em functional-group-based} diffusion model for pocket-specific molecule generation and elaboration. \textsc{D3FG} decomposes molecules into two categories of components: functional groups defined as rigid bodies and linkers as mass points. And the two kinds of components can together form complicated fragments that enhance ligand-protein interactions. To be specific, in the diffusion process, \textsc{D3FG} diffuses the data distribution of the positions, orientations, and types of the components into a prior distribution; In the generative process, the noise is gradually removed from the three variables by denoisers parameterized with designed equivariant graph neural networks. In the experiments, our method can generate molecules with more realistic 3D structures, competitive affinities toward the protein targets, and better drug properties. Besides, \textsc{D3FG} as a solution to a new task of molecule elaboration, could generate molecules with high affinities based on existing ligands and the hotspots of target proteins.