Zhijun Zeng

Liwei Lu, Zhijun Zeng, Yan Jiang et al.

Revealing hidden dynamics from the stochastic data is a challenging problem as randomness takes part in the evolution of the data. The problem becomes exceedingly complex when the trajectories of the stochastic data are absent in many scenarios. Here we present an approach to effectively modeling the dynamics of the stochastic data without trajectories based on the weak form of the Fokker-Planck (FP) equation, which governs the evolution of the density function in the Brownian process. Taking the collocations of Gaussian functions as the test functions in the weak form of the FP equation, we transfer the derivatives to the Gaussian functions and thus approximate the weak form by the expectational sum of the data. With a dictionary representation of the unknown terms, a linear system is built and then solved by the regression, revealing the unknown dynamics of the data. Hence, we name the method with the Weak Collocation Regression (WCR) method for its three key components: weak form, collocation of Gaussian kernels, and regression. The numerical experiments show that our method is flexible and fast, which reveals the dynamics within seconds in multi-dimensional problems and can be easily extended to high-dimensional data such as 20 dimensions. WCR can also correctly identify the hidden dynamics of the complex tasks with variable-dependent diffusion and coupled drift, and the performance is robust, achieving high accuracy in the case with noise added.

Zhijun Zeng, Yixuan Jiang, Pipi Hu et al.

Density estimation is a central primitive in probabilistic modeling, yet continuous, discrete, and mixed-variable domains are often treated by separate objectives, limiting the ability to exploit a common statistical structure across data types. Continuous score-based methods rely on log-density gradients, while discrete extensions typically use concrete score whose unbounded targets become unstable near low-probability states. We introduce Constant-Target Energy Matching (CTEM), a unified energy-based framework for density estimation on general state spaces. CTEM replaces ordinary density-ratio regression with a bounded energy-difference transform and derives from it a sample-only training objective with the constant target 1. The learned scalar potential recovers log p without partition-function estimation or explicit unbounded ratio regression. Across continuous, discrete, and mixed-variable benchmarks, CTEM substantially improves density estimation over competitive baselines and yields higher-quality samples under standard sampling procedures.

Zhijun Zeng, Junqing Chen, Zuoqiang Shi

We study an inverse problem for stochastic and quantum dynamical systems in a time-label-free setting, where only unordered density snapshots sampled at unknown times drawn from an observation-time distribution are available. These observations induce a distribution over state densities, from which we seek to recover the parameters of the underlying evolution operator. We formulate this as learning a distribution-to-function neural operator and propose BlinDNO, a permutation-invariant architecture that integrates a multiscale U-Net encoder with an attention-based mixer. Numerical experiments on a wide range of stochastic and quantum systems, including a 3D protein-folding mechanism reconstruction problem in a cryo-EM setting, demonstrate that BlinDNO reliably recovers governing parameters and consistently outperforms existing neural inverse operator baselines.

Zhijun Zeng, Zhitong Chen, Ling Qin et al.

We propose a Deep-Picard iteration framework for high-dimensional nonlinear space-time fractional diffusion equations.The method is based on a nonlinear fractional Feynman--Kac fixed-point formulation, which replaces direct discretization of the Caputo memory term and the nonlocal fractional Laplacian by Monte Carlo simulation of the associated fractional dynamics. Each Picard update is approximated by stochastic label generation and realized through supervised neural-network regression, thereby avoiding residual minimization involving fractional differential operators. The fractional trajectories are generated by coupling a discretized beta-stable subordinator with a walk-on-spheres-type simulation of the rotationally symmetric alpha-stable Lévy process. Numerical experiments on two-dimensional and high-dimensional test problems ddemonstrate stable Picard convergence and accurate approximation, with tests reported up to dimension d=100.

Gongbo Zhang, Yanting Li, Renqian Luo et al. · microsoft-research

Function in natural systems arises from one-dimensional sequences forming three-dimensional structures with specific properties. However, current generative models suffer from critical limitations: training objectives seldom target function directly, discrete sequences and continuous coordinates are optimized in isolation, and conformational ensembles are under-modeled. We present UniGenX, a unified generative foundation model that addresses these gaps by co-generating sequences and coordinates under direct functional and property objectives across proteins, molecules, and materials. UniGenX represents heterogeneous inputs as a mixed stream of symbolic and numeric tokens, where a decoder-only autoregressive transformer provides global context and a conditional diffusion head generates numeric fields steered by task-specific tokens. Besides the new high SOTAs on structure prediction tasks, the model demonstrates state-of-the-art or competitive performance for the function-aware generation across domains: in materials, it achieves "conflicted" multi-property conditional generation, yielding 436 crystal candidates meeting triple constraints, including 11 with novel compositions; in chemistry, it sets new benchmarks on five property targets and conformer ensemble generation on GEOM; and in biology, it improves success in modeling protein induced fit (RMSD < 2 Å) by over 23-fold and enhances EC-conditioned enzyme design. Ablation studies and cross-domain transfer substantiate the benefits of joint discrete-continuous training, establishing UniGenX as a significant advance from prediction to controllable, function-aware generation.

Zhijun Zeng, Yihang Zheng, Youjia Zheng et al.

Ultrasound Computed Tomography (USCT) provides a radiation-free option for high-resolution clinical imaging. Despite its potential, the computationally intensive Full Waveform Inversion (FWI) required for tissue property reconstruction limits its clinical utility. This paper introduces the Neural Born Series Operator (NBSO), a novel technique designed to speed up wave simulations, thereby facilitating a more efficient USCT image reconstruction process through an NBSO-based FWI pipeline. Thoroughly validated on comprehensive brain and breast datasets, simulated under experimental USCT conditions, the NBSO proves to be accurate and efficient in both forward simulation and image reconstruction. This advancement demonstrates the potential of neural operators in facilitating near real-time USCT reconstruction, making the clinical application of USCT increasingly viable and promising.

Zhijun Zeng, Youjia Zheng, Hao Hu et al.

Accurate and efficient simulation of wave equations is crucial in computational wave imaging applications, such as ultrasound computed tomography (USCT), which reconstructs tissue material properties from observed scattered waves. Traditional numerical solvers for wave equations are computationally intensive and often unstable, limiting their practical applications for quasi-real-time image reconstruction. Neural operators offer an innovative approach by accelerating PDE solving using neural networks; however, their effectiveness in realistic imaging is limited because existing datasets oversimplify real-world complexity. In this paper, we present OpenBreastUS, a large-scale wave equation dataset designed to bridge the gap between theoretical equations and practical imaging applications. OpenBreastUS includes 8,000 anatomically realistic human breast phantoms and over 16 million frequency-domain wave simulations using real USCT configurations. It enables a comprehensive benchmarking of popular neural operators for both forward simulation and inverse imaging tasks, allowing analysis of their performance, scalability, and generalization capabilities. By offering a realistic and extensive dataset, OpenBreastUS not only serves as a platform for developing innovative neural PDE solvers but also facilitates their deployment in real-world medical imaging problems. For the first time, we demonstrate efficient in vivo imaging of the human breast using neural operator solvers.

Liya Guo, Liwei Lu, Zhijun Zeng et al.

With the rapid increase of observational, experimental and simulated data for stochastic systems, tremendous efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the broad applications of non-Gaussian fluctuations in numerous physical phenomena, the data-driven approaches to extracting stochastic dynamics with Lévy noise are relatively few. In this work, we propose a Weak Collocation Regression (WCR) to explicitly reveal unknown stochastic dynamical systems, i.e., the Stochastic Differential Equation (SDE) with both $α$-stable Lévy noise and Gaussian noise, from discrete aggregate data. This method utilizes the evolution equation of the probability distribution function, i.e., the Fokker-Planck (FP) equation. With the weak form of the FP equation, the WCR constructs a linear system of unknown parameters where all integrals are evaluated by Monte Carlo method with the observations. Then, the unknown parameters are obtained by a sparse linear regression. For a SDE with Lévy noise, the corresponding FP equation is a partial integro-differential equation (PIDE), which contains nonlocal terms, and is difficult to deal with. The weak form can avoid complicated multiple integrals. Our approach can simultaneously distinguish mixed noise types, even in multi-dimensional problems. Numerical experiments demonstrate that our method is accurate and computationally efficient.

Zhijun Zeng, Weiye Gan, Junqing Chen et al.

In many engineering and applied science domains, high-dimensional nonlinear filtering is still a challenging problem. Recent advances in score-based diffusion models offer a promising alternative for posterior sampling but require repeated retraining to track evolving priors, which is impractical in high dimensions. In this work, we propose the Conditional Score-based Filter (CSF), a novel algorithm that leverages a set-transformer encoder and a conditional diffusion model to achieve efficient and accurate posterior sampling without retraining. By decoupling prior modeling and posterior sampling into offline and online stages, CSF enables scalable score-based filtering across diverse nonlinear systems. Extensive experiments on benchmark problems show that CSF achieves superior accuracy, robustness, and efficiency across diverse nonlinear filtering scenarios.

Zhijun Zeng, Youjia Zheng, Chang Su et al.

Tissue mechanics--stiffness, density and impedance contrast--are broadly informative biomarkers across diseases, yet routine CT, MRI, and B-mode ultrasound rarely quantify them directly. While ultrasound tomography (UT) is intrinsically suited to in-vivo biomechanical assessment by capturing transmitted and reflected wavefields, efficient and accurate full-wave scattering models remain a bottleneck. Here, we introduce a generative neural physics framework that fuses generative models with physics-informed partial differential equation (PDE) solvers to produce rapid, high-fidelity 3D quantitative imaging of tissue mechanics. A compact neural surrogate for full-wave propagation is trained on limited cross-modality data, preserving physical accuracy while enabling efficient inversion. This enables, for the first time, accurate and efficient quantitative volumetric imaging of in vivo human breast and musculoskeletal tissues in under ten minutes, providing spatial maps of tissue mechanical properties not available from conventional reflection-mode or standard UT reconstructions. The resulting images reveal biomechanical features in bone, muscle, fat, and glandular tissues, maintaining structural resolution comparable to 3T MRI while providing substantially greater sensitivity to disease-related tissue mechanics.

Zhijun Zeng, Pipi Hu, Chenglong Bao et al.

In this paper, we study the method to reconstruct dynamical systems from data without time labels. Data without time labels appear in many applications, such as molecular dynamics, single-cell RNA sequencing etc. Reconstruction of dynamical system from time sequence data has been studied extensively. However, these methods do not apply if time labels are unknown. Without time labels, sequence data becomes distribution data. Based on this observation, we propose to treat the data as samples from a probability distribution and try to reconstruct the underlying dynamical system by minimizing the distribution loss, sliced Wasserstein distance more specifically. Extensive experiment results demonstrate the effectiveness of the proposed method.

Zhijun Zeng, Zhen Hou, Ting Li et al.

We develop a deep learning approach to predicting a set of ventilator parameters for a mechanically ventilated septic patient using a long and short term memory (LSTM) recurrent neural network (RNN) model. We focus on short-term predictions of a set of ventilator parameters for the septic patient in emergency intensive care unit (EICU). The short-term predictability of the model provides attending physicians with early warnings to make timely adjustment to the treatment of the patient in the EICU. The patient specific deep learning model can be trained on any given critically ill patient, making it an intelligent aide for physicians to use in emergent medical situations.