召集人：张宏坤（大湾区大学，理学院，教授）、夏志宏（大湾区大学，理学院，教授）、陈剑宇（苏州大学，数学科学学院，教授）

时间：2026.03.08—2026.03.14

会议报告安排表

注：周二、周四下午茶歇后的每个报告为30分钟

会议日程

报告题目和摘要

(按姓氏拼音字母序排列) 

Why you should consider using Isolation Kernel and Isolation Distributional Kernel

陈开明（南京大学）

Abstract:  The talk presents some successful applications of Isolation Kernel (IK) and Isolation Distributional Kernel (IDK). IK measures the similarity between two points/vectors. IK is better than the commonly used Euclidean distance and Gaussian kernel because of three unique characteristics. First, IK measures two points in a sparse region to be more similar than two points of the same inter-point distance in a dense region. This enables similarity to be compared more effectively in a dataset with varied densities. Second, IK is the only measure that has been proven to have broken the curse of dimensionality. This enables IK to deal with high-dimensional datasets more effectively than other measures. Third, IK has a finite-dimensional feature map, and this allows it to be computed more efficiently than other kernels. IDK is derived from IK to measure the similarity between two distributions, and it inherits the above characteristics of IK.

This presentation provides IK's successful applications to (a) improving t-SNE visualization and (b) retrieval in high-dimensional datasets. IDK has been successfully applied to (i) anomaly detection: creating a detector which is more effective than Isolation Forest---one of the most popular detectors used in industry and academia; and (ii) clustering: converting an NP-hard problem into a linear-time problem. A brief history of isolation-based methods can be found at  https://github.com/IsolationKernel

Data-driven Discovery of Asymmetric Interacting Particle Systems

冯锦超（大湾区大学）

Abstract:  Interacting particle systems provide a powerful modeling framework for collective dynamics in nature and engineering. While prior methods have primarily addressed symmetric interactions using various learning techniques, many real-world systems exhibit asymmetric interactions, which demand more general and flexible modeling tools. In this talk, I will present a new Sparse Bayesian Learning (SBL) framework for identifying asymmetric interaction kernels in the Motsch–Tadmor model. By reformulating the nonlinear inverse problem as a subspace identification task, we establish identifiability guarantees and enable robust kernel recovery. Incorporating informative priors, the proposed SBL algorithm offers principled model selection and uncertainty quantification, achieving reliable inference from noisy trajectory data.

Twist Dynamics in the Spatial Isosceles Three-body Problem

胡锡俊（山东大学）

Abstract:  We study dynamical constraints arising from Embedded Contact Homology (ECH) in the spatial isosceles three-body problem. For energies below the critical level, the dynamics on the energy surface is identified with a Reeb flow on the tight three-sphere. We obtain quantitative estimates for the Euler orbit, including monotonicity of its transverse rotation number and a strict inequality comparing its action with the contact volume. Combined with the ECH classification of Reeb flows on the tight three-sphere with two simple periodic orbits, these estimates rule out the two-orbit scenario, thus forcing every compact energy surface below the critical level to have infinitely many periodic orbits. The result admits a dynamical interpretation via disk-like global surfaces of section bounded by the Euler orbit. In this setting, the rotation number and the contact volume define a non-trivial twist interval which encodes the relative winding of periodic orbits.

Nonlinear Transformation Based Infinite-Dimensional Variational Inference for Statistical Inverse Problems

贾骏雄（西安交通大学）

Abstract:  Inverse problems for PDEs are ubiquitous across scientific disciplines and can be formulated as statistical inference problems via Bayes’ theorem. For large-scale problems, the development of discretization-invariant algorithms is crucial, which can be achieved by formulating the methods in infinite-dimensional spaces. By restricting the variational family to be the pushforward of a nonlinear transformation of the prior measure, one obtains various classes of variational inference methods. By overcoming the singularity issues associated with probability measures defined on infinite-dimensional function spaces, we develop two such methods, termed infinite-dimensional Stein variational gradient descent (iSVGD) and functional normalizing flows (FNF). The transformations constructed in both iSVGD and FNF consist of a sequence of perturbations of the identity operator. In iSVGD, the perturbation mappings belong to an appropriate reproducing kernel Hilbert space, whereas in FNF, they are constructed using carefully designed neural network architectures. We apply these algorithms to an inverse problem governed by the steady-state Darcy flow equation. Numerical results validate the theoretical analysis, demonstrate the efficiency of the proposed algorithms, and confirm their discretization-invariant properties.

如何实现跨模型互学？

蒋建成（大湾区大学）

Abstract:  现有高维线性回归的迁移学习方法受限于源域与目标域的特征需严格对应，这在特征形式不同（如临床评分与传感器数据）但共享预测信号的现实场景中往往不适用。为此，我们提出跨模型迁移学习（CMTL）框架。CMTL通过构建数据自适应的权重矩阵，密集连接所有源与目标模型系数，以解析方式增强稳定源信号的迁移并抑制噪声，无需预先指定特征对应关系。理论上，CMTL在标准条件下达到了Oracle效率；实证中，其在仿真与实际预测任务上均显著优于现有基线方法，在传统方法失效时表现出鲁棒性。

基于交互式信号通路的基因表达随机动力学推断

焦锋（广州大学）

Abstract:  我们对交互式信号路径调控的基因表达研究，源于病原体调控蚊子、果蝇及人体先天免疫系统中抗菌肽基因表达的生理现象。单细胞转录随机动力学模型的核心思路，是引入基因在闭合与开启状态间的随机切换，通过模型中多基因状态的串联结构，精准刻画基因激活后有序发生的生化反应过程。针对传统模型的固有局限，我们构建了含多状态并联结构的交互式信号路径转录模型，结合大规模实验数据揭示了具有普适性的转录调控机制，并建立了一套新的参数估计与模型筛选方法。

TS-PINNs: Physics-Informed Neural Networks in Temporal Sobolev Spaces

李明坤（大湾区大学）

Abstract:  We propose TS-PINNs, a novel class of physics-informed neural networks that incorporate temporal Sobolev regularization to enhance the accuracy, stability, and generalization of neural PDE solvers. Unlike standard PINNs that penalize residuals only at discrete points, TS-PINNs leverage the structure of Sobolev spaces to enforce smoothness in time by explicitly regularizing higher-order temporal derivatives of the solution. This approach improves numerical stability, mitigates error accumulation in long-time integration, and leads to physically consistent approximations for time-dependent differential equations.

The TS-PINN framework is implemented in a multi-stage training procedure, where earlier stages learn temporally coarse solutions, and later stages refine them using higher-order constraints derived from the governing PDE. We provide theoretical motivation based on functional approximation theory in Sobolev spaces, and we empirically validate the method on several benchmark problems, including the Burgers equation and nonlinear wave propagation. Across all tasks, TS-PINNs demonstrate improved accuracy, enhanced robustness to noise, and faster convergence relative to classical PINNs and recent variants. Our results show that temporal Sobolev regularization provides a principled and practical enhancement to physics-informed learning of time-evolving systems.

利用概率深度学习重构和预测随机动力系统

林媛（山西大学）

Abstract:  现实动力系统往往受到随机噪声干扰。这种随机性破坏了确定性嵌入的拓扑结构，导致基于确定性延迟嵌入理论的点到点映射模型在处理带噪数据时，会出现重构或预测失效。如何利用深度学习方法有效地表征随机动力系统的相空间的重构映射是当前该领域的关键问题。提出了一种融合随机动力系统先验与概率深度学习的新型框架，基于随机延迟嵌入定理，构建了深度随机延迟嵌入计算模型，利用随机过程的变分近似，重构了随机动力系统以实现了稳健的长期预测。

Temporal Convolution-Based Physics-Informed Neural Networks for Solving Forward and Inverse Problems of Time Fractional Partial Differential Equations

蒲哲（大湾区大学）

Abstract:  In this talk, we focuses on establishing the efficient computational framework for sloving time fractional partial differential equations (PDEs) by combining physical information neural networks (PINNs). Since the  automatic differentiation is not applicable for fractional derivatives, the numerical discretization scheme of fractional derivatives is introduced by Pang et al. (2019) called fPINNs. However, this approach faces serious efficiency bottlenecks in non local historical calculations, the standard fPINNs construction evaluates a discrete fractional operator through nested history summations, leading to $O(N^2)$ work per spatial sample over $N$ time levels with high complexity and computational cost. We propose the fractional PINNs framework called Convolution-fPINNs based on convolutional structure for numerical discretization formula  and Fourier Transform method,  which can significantly reduces the computational complexity to $O(N\log N)$ while strictly maintaining the mathematical equivalence with the numerical discretization formula. We couple this accelerated framework with  PINNs  and demonstrate the effectiveness of such method on forward solution and inverse parameter identification tasks for  time-fractional advection--diffusion equations with highly nonlinear operator. Numerical results show that  the Convolution-fPINNs method can effectively solve both the forward and inverse problems of high-dimensional time fractional PDEs, and achieves significant computational efficiency improvement while ensuring the accuracy compared to fPINNs.

Identifying phase transition types in epidemic network dynamics via deep learning

 申建伟（华北水利水电大学）

Abstract:  Traditional statistical indicators face challenges in identifying phase transition types in epidemic dynamics on complex networks due to strong structural dependence and limited generalization capability. To address this issue, this paper proposes a deep learning framework that integrates network topology with node-level dynamical information. Based on a generalized SIS model, we construct four typical propagation scenarios (pairwise-only transmission, higher-order synergistic transmission only, mixed transmission, and cases with exogenous driving) and systematically generate dynamical samples labeled as first-order phase transition, second-order phase transition, or no transition. To mimic real-world observations, all model inputs are strictly truncated to the pre-transition period using node-level residual sequences, ensuring no future information leakage. The model adopts an end-to-end architecture combining graph convolutional networks (GCN), attention pooling, and long short-term memory (LSTM) networks. It encodes network structure via the adjacency matrix and constructs a dual-channel temporal input consisting of node residuals and their first-order differences to enhance the extraction of precursory dynamical features. Experimental results on Watts–Strogatz small-world networks demonstrate that the proposed method effectively distinguishes different phase transition types, significantly outperforming a CNN-LSTM baseline built on 12 handcrafted spatiotemporal indicators, particularly in discriminating first-order from second-order transitions. Ablation studies further reveal that the closer the truncation point to the critical transition, the higher the classification accuracy, indicating that pre-transition dynamics contain rich discriminative information about the transition type. This study provides a feasible pathway for intelligent identification of phase transition types in epidemic dynamics on complex networks and offers methodological support for early warning and intervention strategy design under higher-order synergistic transmission mechanisms.

PD-Outsoured PINN —— 一种新的求解PDE的PINN方法

石剑平（昆明理工大学）

Abstract:  Solving partial differential equations (PDEs) has always been a challenging issue in scientific research, especially when there are fractional-order derivatives in the equations. This paper proposes a new method for solving α (α ≤ 1)-order PDEs based on the physical information neural network (PINN): Portion-Derivative Outsourced PINN (PD-Outsourced PINN) framework. This framework introduces a analytical module to handle the α-order differential term, enabling the PINN to focus on learning the remaining part of the equation. Furthermore, the results of the analytical module is incorporated into the loss function of the PINN for correcting the network parameters. Three (1+1)-dimensional and two (2+1)-dimensional equations are used to validate the effectiveness and reliability of this method. The results show that, given the initial and boundary values of the PDEs, by combining the constructed analytical basis function and the output solution of the PINN, this method can obtain the high-precision data-driven solutions of the original equation. The PD-Outsourced PINN provides a high precision, good convergence, and strong robustness approach for solving complex PDEs.

基于Koopman理论的连续谱动力系统表示与预测方法

束俊（西安交通大学）

Abstract:  对高维时空混沌动力系统进行表示与预测，仍然是动力系统理论与机器学习领域中的一个基础性挑战。高维、非线性且具有连续谱结构的动力系统广泛存在于气候演化、湍流流动、复杂网络传播以及神经动力学等现实场景中。尽管目前数据驱动方法能够实现较为准确的短期预测，但在以宽频或连续谱为主导的系统中，它们往往缺乏稳定性、可解释性和可扩展性。Koopman 理论为非线性动力学的表征和预测提供了一个线性化视角，但现有方法通常依赖于有限维逼近，这在高维场景下往往导致性能退化。本报告提出一种新的神经Koopman方法，通过将可逆运动与不可逆耗散分离，实现对动力系统的结构化表示。该方法在提高长期预测精度与稳定性的同时，也有助于揭示混沌行为中哪些方面是可以被理解和学习的。

可控生成建模的数学基础与交叉应用

孙剑（西安交通大学）

Abstract:  生成式人工智能是当前通用人工智能发展的重要方向，主要通过设计人工智能算法实现对多模态、高维复杂样本分布的学习与新样本的生成，是当前人工智能应用于自动问答、跨模态生成、AI for science等问题的方法基础。生成式人工智能的底层基础是数学与统计学，本报告主要介绍生成式人工智能的背景、数学／统计学原理以及面临的挑战，进一步介绍以最优传输作为基础来构建可控／条件生成的人工智能方法，并应用于医学影像生成、多模态图像文本对齐、分子结构生成等问题，最终总结与展望生成式人工智能的发展与前景。

面向生物医学的视觉-语言模型的因果条件提示学习

王如心（中国科学院深圳先进技术研究院）

Abstract:  本报告聚焦面向生物医学领域的视觉-语言模型，探讨基于提示学习的大模型微调方法及其在生物医学上的应用。针对生物医学数据多模态、标注稀缺等特点，引入因果干预以增强提示学习的可解释性与泛化能力，有效缓解数据偏差与伪相关。通过在预训练模型基础上进行参数高效微调，实现视觉特征与临床文本知识的深度对齐，显著提升模型在医学图像分析、分子表示、跨模态检索等任务中的性能。

Mathematical Methods in Data Science

夏志宏（大湾区大学）

Abstract:  We discuss some fundamental mathematical theory behind data science and AI, including approximation theory and a new complexity theory for data.

Modelling heterogeneities in disease transmission dynamics

肖燕妮（西安交通大学）

Abstract:  Accurate prediction of epidemics is pivotal for making well-informed decisions for the control of infectious diseases, but modelling heterogeneity in the system becomes a challenge. In this talk, we propose a novel modelling framework integrating the spatio-temporal heterogeneity of susceptible individuals into homogeneous models, by introducing a continuous recruitment process for the susceptibles. Then, a general human heterogeneous disease model with mutation is proposed to comprehensively study the effects of human heterogeneity on basic reproduction number, final epidemic size and herd immunity. We show that human heterogeneity may increase or decrease herd immunity level, strongly depending on some convexity of the heterogeneity function.  Finally, we illustrate how to link the deep learning to dynamic model to examine time-dependent transmission rate or the intensity of interventions.

长时序列预测：挑战与展望

徐增林（复旦大学）

Abstract:  在多变量时间序列预测领域，精确预测长期趋势在从气候科学到金融市场等众多领域中扮演着关键角色。随着动态系统复杂性的不断增加以及不同领域时序数据的激增，迫切需要解决时间序列数据中固有的复杂依赖关系和时间不确定性问题，并阐明时间序列动态变化机制。本报告概述了我们的最新研究工作，从这些挑战出发，讲述几个不同的工作，分别来探讨时间序列的解耦、时间序列变量间的依赖关系的建模方法，探讨多变量时间序列机制的预测机制，并提出将时间序列分析中的时间演化视为类似于偏微分方程描述的物理过程的连续流动。最后将辨析物理机理驱动与数据驱动范式的优势边界，并展望长时间序列预测从 “黑箱拟合” 走向 “可解释、可泛化、可机理融合” 思路与技术路径。

Rhythm-ONet: A query-conditioned neural operator for high-fidelity emulation of multiscale rhythm transitions in neurological disorder modeling

闫思璐（大湾区大学）

Abstract:  Mechanistic neural mass models (NMMs) are pivotal for digital twins in neurological disorder modeling, offering the potential for diagnosis and treatment of abnormal rhythms associated with Alzheimer’s disease (AD) and epilepsy. However, their solutions can change sharply with synaptic connectivity, making numerical parameter sweeps computationally expensive, while standard neural operator surrogates struggle with spectral bias in resolving these multi-frequency dynamics. We introduce Rhythm-ONet, a query-conditioned neural operator with a time-conditioned coefficient generator in the branch pathway. Inspired by attention mechanisms, the design dynamically reweights branch features according to query points, mitigating spectral bias in operator learning. Combined with a Fourier-embedded trunk, it enables high-fidelity reconstruction of multiscale NMM dynamics. On two canonical NMMs, including the Jansen-Rit system for Alzheimer’s-like activity and the Wendling-Chauvel system for seizure-like dynamics,  Rhythm-ONet achieves substantially lower relative L2 error than DeepONet, Fourier-DeepONet, and DeepONet-Bt, yielding superior time-frequency agreement across synaptic connectivity regimes. Once trained, the emulator enables rapid mapping of synaptic connectivity dependent rhythm transitions, including in silico signatures of rhythm slowing in AD and ictal-like discharges within these mechanistic models.

Numerically Efficient Methods for Solving High-dimensional PDE and Probabilistic Modeling

杨斯崑（大湾区大学）

Abstract:  This report presents numerically efficient methods for solving high-dimensional partial differential equations (PDEs) and their applications in probabilistic modeling, with a focus on score-based generative models. We discuss Cauchy Networks (CauchyNets), a novel single-layer feedforward neural architecture inspired by the Cauchy's integral theorem from complex analysis. The Cauchy activation function provides a principled functional basis for approximating analytic functions in high-dimensional spaces with theoretical approximation guarantees of order O((1/m)ˆk) for any integer K. We integrate CauchyNets with the deep backward stochastic differential equation (BSDE) framework to solve semilinear parabolic PDEs, including Hamilton-Jacobi-Bellman equations arising from stochastic control problems. Numerical experiments demonstrate that a CauchyNet-BSDE solver with only 10 hidden units achieves competitive performance compared to traditional deep BSDE approaches requiring larger architectures. The methodology extends to score-based generative modeling through an important connection: the Fokker-Planck equation governing diffusion processes  via Hopf-Cole transform to a Hamilton-Jacobi-Bellman equation, enabling PDE-based solutions for learning generative models. We parameterize the negative log-density using CauchyNets with time embedding, demonstrating effectiveness on high-dimensional Gaussian mixture densities. Finally, we address the computational challenge of sampling in score-based generative models by developing fast sampling strategies based on probability flow ODEs and fixed-point iteration. These approaches reduce sampling steps by more than 50% (from 50 to 22-25 steps) in video generation models including Open-Sora 1.3 and 2.0, while maintaining generation quality.

Revisiting Smale’s 18th Problem in the Age of Artificial Intelligence

姚远（香港科技大学）

Abstract:  In 1998, Steve Smale proposed his 18th mathematical problem for the 21st century, calling for a deeper understanding of the fundamental limitations of intelligence. Rapid advances in artificial intelligence over the past decade have lent renewed urgency to this challenge, underscoring the need for principled theoretical frameworks that characterize the capabilities and limitations of modern learning systems. The structural differences between human intelligence and contemporary artificial intelligence models shed light on central issues in the development of trustworthy AI, including robustness, interpretability, uncertainty quantification, and computational efficiency. In this talk, I examine these questions through through the lens of topology learning, dynamical systems, optimization algorithms, and statistical inference.

From Approximation to Disentanglement: Trainable Gaussian Mixture Modules for Modern Neural Architectures

苑罡男（云南大学）

Abstract:  Neural networks in general, from MLPs and CNNs to attention-based Transformers, are constructed from layers of linear combinations followed by nonlinear operations such as ReLU, Sigmoid, or Softmax. Despite their strength, these conventional designs are often limited in introducing non-linearity by the choice of activation functions. In this work, we introduce Gaussian Mixture-Inspired Nonlinear Modules (GMNM), a new class of differentiable modules that draw on the universal density approximation Gaussian mixture models (GMMs) and distance properties (metric space)  of Gaussian kernal.

动物机器人的运动行为控制

郑能干（浙江大学）

Abstract:  动物大脑和计算机之间可以借助植入式脑机接口建立直接连接关系，构成以动物为本体、融合计算机的动物机器人。这类机器人的运动行为控制，需要考虑如何对动物大脑进行神经调控、如何建立穿戴轻便的脑机微系统、如何自主产生运动调控指令等问题。通过解决这些问题，有望研制出系统结构简单、感知运动能力优越、系统能耗低、隐蔽性能好的动物机器人，适用于狭小空间探测，也可作为感知-运动神经机制、群组协同控制等基础科学问题的研究对象和研究工具。我们通过探索动物载体的运动行为调控机理，优化动物机器人系统构成，实现了“熊蜂机器人无线运动控制”、“大鼠机器人无人机导航”。

生物医学的多尺度多模态融合技术

郑旭彬（大湾区大学）

Abstract:  脑胶质瘤是起源于脑部的神经胶质细胞的一类肿瘤，胶质母细胞瘤(GBM)是其中最恶性的类型，5年死亡率达95%。GBM的术前风险预测有助于治疗方案的决策。GBM的临床数据涉及磁共振影像（毫米级）、细胞状态（微米级）、基因（纳米级）多种模态和多种尺度，如何整合多模态多尺度数据实现GBM的早期无创风险预测是一个亟待解决的问题。在此，我们将介绍课题组近期在多模态多尺度生物医学数据整合的进展。首先，我们基于提示学习、影像解耦等方式将脑磁共振影像与基因表达进行整合，构建GBM早期无创风险预测模型。然而，由于基因粒度过细，导致影像与基因尺度差距过大，因此，我们提出了生物信息神经网络（BINN），将功能相似的基因进行整合形成基因功能团。此外，我们还使用了胶囊网络和迁移学习利用基因功能团代表单细胞，并辅助以人为样本的数据进行疾病诊断。但由于细胞还收到外部环境的影响，我们构建了空间多模态整合模型SMART，实现了多层次组学与细胞环境的统一表征，为将来实现GBM的准确风险分层奠定基础。

Weak Generative Sampler

周翔（香港城市大学）

Abstract:  Sampling invariant distributions from an Ito diffusion process presents a significant challenge in stochastic simulation. The current deep learning-based method solves the stationary Fokker--Planck equation to determine the invariant probability density function in the form of deep neural networks, but they generally do not directly address the problem of sampling from the computed density function. In this work, we introduce a framework that employs a weak generative sampler (WGS) to directly generate independent and identically distributed (iid) samples induced by a transformation map derived from the stationary Fokker--Planck equation. Our proposed loss function is based on the weak form of the Fokker--Planck equation, integrating normalizing flows to characterize the invariant distribution and facilitate sample generation from a base distribution. Our randomized test function circumvents the need for min-max optimization in the traditional weak formulation. Our method necessitates neither the computationally intensive calculation of the Jacobian determinant nor the invertibility of the transformation map. A crucial component of our framework is the adaptively chosen family of test functions in the form of Gaussian kernel functions with centers related to the generated data samples.

Graph Hamiltonian network: A robust model for learning particle interactions in lattice systems

祖建（东北师范大学）

Abstract:  Addressing the challenges posed by nonlinear lattice models, which are vital across diverse scientific disciplines, in this talk, we introduce separable graph Hamiltonian networks (α-SGHN) that reveals complex interaction patterns between particles in lattice systems. Utilizing trajectory data, α-SGHN infers potential interactions without prior knowledge about particle coupling, overcoming the limitations of traditional graph neural networks that require predefined links. Furthermore, α-SGHN preserves all conservation laws during trajectory prediction. Experimental results demonstrate that α-SGHN, incorporating structural information, outperforms baseline models based on conventional neural networks in predicting lattice systems. This work is in collaboration with Ru Geng, Yixian Gao, Hong-Kun Zhang and Panayotis Kevrekidis.