arXiv subjects

Xingjian Xu

Publications and source records attributed to Xingjian Xu.

6 recordsLinked to original sources

arXiv2026

Persistent Manifold Learning of Protein Properties

Predicting how tightly two biomolecules bind remains a major challenge, in part because different interaction classes present dissimilar interfaces, from compact metal-coordinated pockets to broad, featureless protein surfaces. We introduce persistent manifold learning (PML), a novel computational framework that describes a binding interface as a family of multiscale manifolds. Boundary-Induced Graph Laplacian, a discrete realization of de Rham-Hodge theory, then extracts topological invariants together with nonharmonic spectral information, capturing the geometry of an interface as well as its topology. These manifold embeddings are combined with protein and molecular language model representations and paired with gradient boosting decision trees. Our PML outperforms state-of-the-art methods on metalloprotein-ligand and protein-protein benchmarks.

q-bio.BM↗

arXiv2026

The finite expression method for turbulent dynamics with high-order moment recovery

Turbulent dynamical systems are characterized by nonlinear interactions and stochastic effects that generate coupled statistical quantities, such as non-zero higher-order moments, which are difficult to capture from data with accuracy. We propose a two-stage data-driven modeling framework that combines symbolic regression with generative models to jointly identify the governing dynamics and predict their key statistical quantities. In Stage I of the framework, the Finite Expression Method (FEX) is adopted to discover closed-form expressions of the deterministic dynamics, recovering nonlinear interaction terms and external forcing without predefined libraries. In Stage II, generative models are introduced to learn the residual stochastic components as a refined correction to the model error from the Stage I approximation, enabling accurate characterization of higher-order statistics. Theoretical analysis establishes the consistency of the symbolic estimator and quantifies the estimation error in terms of data size and numerical discretization. The model performance is verified through detailed numerical experiments on the stochastic triad models across multiple regimes, demonstrating that the framework successfully recovers interaction terms and forcing expressions, and accurately predicts statistical moments up to order five. These results highlight the potential of integrating interpretable symbolic discovery with data-driven stochastic modeling for complex turbulent systems.

cs.LG↗

arXiv2025

Identifying Unknown Stochastic Dynamics via Finite expression methods

Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a combination of deterministic and stochastic terms. However, these models usually lack interpretability and have difficulty generalizing beyond their training domain. This paper introduces the Finite Expression Method (FEX), a symbolic learning approach designed to derive interpretable mathematical representations of the deterministic component of SDEs. For the stochastic component, we integrate FEX with advanced generative modeling techniques to provide a comprehensive representation of SDEs. The numerical experiments on linear, nonlinear, and multidimensional SDEs demonstrate that FEX generalizes well beyond the training domain and delivers more accurate long-term predictions compared to neural network-based methods. The symbolic expressions identified by FEX not only improve prediction accuracy but also offer valuable scientific insights into the underlying dynamics of the systems, paving the way for new scientific discoveries.

cs.LG↗

arXiv2024

PLD-Tree: Persistent Laplacian Decision Tree for Protein-Protein Binding Free Energy Prediction

Recent advances in topology-based modeling have accelerated progress in physical modeling and molecular studies, including applications to protein-ligand binding affinity. In this work, we introduce the Persistent Laplacian Decision Tree (PLD-Tree), a novel method designed to address the challenging task of predicting protein-protein interaction (PPI) affinities. PLD-Tree focuses on protein chains at binding interfaces and employs the persistent Laplacian to capture topological invariants reflecting critical inter-protein interactions. These topological descriptors, derived from persistent homology, are further enhanced by incorporating evolutionary scale modeling (ESM) from a large language model to integrate sequence-based information. We validate PLD-Tree on two benchmark datasets-PDBbind V2020 and SKEMPI v2 demonstrating a correlation coefficient ($R_p$) of 0.83 under the sophisticated leave-out-protein-out cross-validation. Notably, our approach outperforms all reported state-of-the-art methods on these datasets. These results underscore the power of integrating machine learning techniques with topology-based descriptors for molecular docking and virtual screening, providing a robust and accurate framework for predicting protein-protein binding affinities.

q-bio.BM↗

arXiv2023

Deep Learning via Neural Energy Descent

This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulated as the evolution of network parameters in an evolution equation and the steady state solution of the partial differential equation (PDE) provides a solution to deep learning. This equation corresponds to a gradient descent flow of a variational problem and hence the proposed time-dependent PDE solves an energy minimization problem to obtain a global minimizer of deep learning. This gives a novel interpretation and solution to deep learning optimization. The computational complexity of the proposed energy descent method can be enhanced by randomly sampling the spatial domain of the PDE leading to an efficient NED. Numerical examples are provided to demonstrate the numerical advantage of NED over stochastic gradient descent (SGD).

math.NA↗

arXiv2022

Discovery of subdiffusion problem with noisy data via deep learning

Data-driven discovery of partial differential equations (PDEs) from observed data in machine learning has been developed by embedding the discovery problem. Recently, the discovery of traditional ODEs dynamics using linear multistep methods in deep learning have been discussed in [Racheal and Du, SIAM J. Numer. Anal. 59 (2021) 429-455; Du et al. arXiv:2103.11488]. We extend this framework to the data-driven discovery of the time-fractional PDEs, which can effectively characterize the ubiquitous power-law phenomena. In this paper, identifying source function of subdiffusion with noisy data using L1 approximation in deep neural network is presented. In particular, two types of networks for improving the generalization of the subdiffusion problem are designed with noisy data. The numerical experiments are given to illustrate the availability using deep learning. To the best of our knowledge, this is the first topic on the discovery of subdiffusion in deep learning with noisy data.

math.NA↗