Interdisciplinary Frontier Workshop on Dynamic Characterized Life Sciences

The 2025 Interdisciplinary Frontier Workshop on Dynamic Characterized Life Sciences organized by Professor Wei Lin(Fudan University), Luonan Chen (Shanghai Jiao Tong University), Ting Gao (Huazhong University of Science and Technology), was successfully held at the Tianyuan Mathematics Research Center from December 7 - 12, 2025.

This forum focuses on cutting-edge interdisciplinary issues between applied mathematics and life sciences (such as brain science, molecular cell biology, gene regulatory networks, etc.). It explores innovative applications of mathematical tools and theories in life sciences, and the driving force of interdisciplinary research in life sciences and medicine-engineering on new methods in applied mathematics.

This forum stimulates interdisciplinary collaboration, promotes the deepening of life science and medical research, and fosters innovation in applied mathematical theories and methods, providing new insights into understanding the complexity of living systems and the development of intelligent systems. Specific areas of focus: 1.Applications of stochastic dynamical systems in life sciences; 2.Mathematical problems and methods in early disease warning, diagnosis, and personalized treatment; 3.Inverse dynamical problems integrating data-driven approaches and biological prior; 4.Causal inference and its applications；5.Mathematical methods in neural regulation and life regulation. Each expert presentation is approximately 50 minutes long. And the total number of talks is 26. Some contents of the talks are:

1. Mechanisms of Neuron and Oscillator Dynamics

Core Content: Starting from integrate-and-fire neurons and pulse-coupled oscillators, a unified threshold-reset dynamics framework is established. In the large-scale limit, non-standard transport-type equations are derived to characterize the connection between microscopic stochastic dynamics and macroscopic statistical descriptions. For voltage-conductance neuron models, exponential convergence of solutions is proven using Harris's theorem through the equivalence of probability processes and kinetic equations.

Methodological Innovation: Bypassing the failure of classical assumptions; introducing time scaling and quantile function reformulation for pulse-coupled oscillators, revealing the correspondence between PRC geometric properties and synchronization behavior.

Open Problems: Global behavior analysis under nonlinear feedback, finite particle number effects, and the influence of network heterogeneity.

2. Molecular-Scale Stochastic Dynamics and Statistical Inference

Core Content: Establishing a theoretical framework for molecular-level stochastic dynamics from Chemical Master Equations (CME) to Stochastic Differential Equations (SDE). CME precisely describes reaction dynamics as Markov jump processes, while SDE achieves continuous approximation through Kramers-Moyal expansion.

Statistical Inference: Facing finite-length, noisy observation trajectories, parameter estimation is achieved by maximizing likelihood or Bayesian posterior distributions. The physical structure of dynamical models plays a decisive role in inference.

Open Problems: Computational challenges in high-dimensional multi-timescale systems, inference algorithms under incomplete observations, and integration of machine learning with classical models.

3. Bistable Potential Landscape Control and Reliable Logic Operations

Core Content: Based on SDEs of overdamped bistable systems, investigating Reliable Logic Operations (RLO) and Logical Stochastic Resonance (LSR) under stochastic perturbations. Steady-state probability distributions are solved via Fokker-Planck equations.

Methodological Innovation: Proposing the control potential method, providing analytical sufficient conditions for RLO for the first time; introducing a survival probability analysis framework to handle bistable scenarios; clarifying two fundamental characteristics: initial value independence and sign invariance.

Open Problems: Multi-stable system control, multi-valued logic generalization, non-Gaussian noise effects, and nanoscale device implementation.

4.  Identifiability and Inference Algorithms for Gene Regulatory Networks

Core Content: Establishing a dual-information model framework (PIM and FIM) for probabilistic Boolean networks, clarifying network identifiability criteria with sample requirements of only O(log n). Developing multiple algorithms to address inherent defects in single-cell and spatial transcriptomics data.

Algorithmic Innovation: NG-SEM adopts Gaussian mixture models to adapt to complex noise; Phi-TargetFlow quantifies direct information flow between genes based on an integrated information decomposition framework.

Open Problems: Complex network identifiability, computational efficiency for ultra-large-scale data, multi-omics integration, and wet-lab experimental validation.

5. Mechanism-Data Fusion Methods for Medical Image Computing

Core Content: Proposing the Variational Image-RRT* framework, transferring path planning algorithms to the image domain. Constraining vascular system modeling based on biological laws such as Murray's law, constructing energy functionals incorporating smoothness, curvature, and gradient guidance.

Methodological Innovation: CNN-embedded architecture enables data-driven enhancement; SAM fusion with Star Shape constraints for weakly supervised ultrasound image segmentation, achieving Dice coefficients of 83-88%.

Open Problems: Complex lesion handling, real-time optimization, cross-modal generalization, few-shot learning, and clinical translation standards.

6.  Memory-Driven AI Modeling of Complex Systems

Core Content: Focusing on Neural Ordinary Differential Equations (Neural ODE), Neural Delay Differential Equations (Neural DDE), Higher-Order Granger Reservoir Computing (HoGRC), Memory-Enhanced Koopman Learning (MERLIN), and Flow Matching (FM) methods.

Methodological Innovation: Neural DDE introduces delay mechanisms to address memoryless limitations; HoGRC achieves simultaneous optimization of structure inference and dynamics prediction (Nature Communications Featured Article); Delay Flow Matching (DFM) solves transport path crossing problems.

Open Problems: Automatic learning of delay parameters, efficient inference of higher-order structures, cross-scale modeling, and physical constraint fusion.

7.  Mathematical Theory and Methods for Complex Biological Systems

Core Content: Centering on three major themes of phase transition bifurcation, system order, and critical characteristics, exploring ecosystem critical transitions, collective oscillation emergence, frequency-amplitude modulation mechanisms, and non-consensus opinion formation. Network dynamics dimension reduction is analyzed based on the FitzHugh-Nagumo model.

Methodological Innovation: Proposing frequency-amplitude coordinators for independent frequency-amplitude modulation (Nature Communications 2021); nonlinear decoupling control strategies (Phys. Rev. Lett. 2023); establishing correspondence between non-consensus opinion intensity and network spectral distribution.

Open Problems: High-dimensional network dimension reduction, global oscillation control optimization, multi-scale unified description, and integration of machine learning with dynamical modeling.

8. Research on Evolutionary Patterns of Cognitive Impairment

Core Content: With Alzheimer's disease as the core, combining multimodal representation learning to construct complete solutions for intelligent screening, fine-grained evolution characterization, and adaptive sequential decision-making. Intelligent scoring is achieved based on the digital Clock Drawing Test (dCDT).

Methodological Innovation: Integrating image geometric features, drawing behavior data, and text semantic features, the AlexNet+Trace combined model achieves 80.65% accuracy; adaptive sequential decision-making dynamically selects optimal questions through information value assessment.

Open Problems: Algorithm interpretability and clinical acceptance, longitudinal tracking data acquisition, precise individual difference modeling, and integration with dynamical methods.

9. Early Warning of Critical Transitions in Nonlinear Stochastic Systems

Core Content: Proposing warning indicators using relaxation time instead of traditional recovery time, validated in lake ecology, self-organized systems, and tumor-immune systems. Innovating machine learning framework based on surrogate data (SDML).

Methodological Innovation: Relaxation time requires no system perturbation; SDML breaks through bifurcation assumption dependencies, achieving high-precision warning with small samples, with fold bifurcation prediction accuracy reaching 0.77 (Communications Physics, Science Featured report).

Open Problems: Warning for non-stationary systems, multi-stable system handling, warning time window optimization, and integration with intervention strategies.

10. Causal Inference of Cell State Transitions

Core Content: Introducing CIBER and CausLens, two causal inference algorithms. CIBER achieves causal network reconstruction and cell fate determinant identification at the cell type level; CausLens focuses on causal dimension reduction and trajectory inference at the single-cell level.

Methodological Innovation: CIBER is based on Bayesian network structure learning and structural causal models, possessing anti-missingness and generalization properties; CausLens achieves silhouette coefficient of 0.243, outperforming original methods (0.127); WAVERSE achieves omics data augmentation through graph wavelet transform.

Open Problems: Reliable causal direction determination, hidden variable handling, temporal resolution improvement, integration with perturbation experiments, and biological validation.

Summary and Outlook

Common Methodology: All reports demonstrate multi-scale modeling thinking from microscopic mechanisms to macroscopic behavior, emphasizing methodological innovations including probability process-partial differential equation equivalence, spatiotemporal information transformation, control estimation techniques, and causal inference.

Core Paradigm: Organically integrating stochastic dynamics modeling, scale limit analysis with machine learning/deep learning, achieving breakthroughs from static data to dynamic laws.

Key Challenges: Multi-modal multi-scale data fusion, causal relationship reliability verification, model interpretability and clinical translation, computational efficiency and scalable applications. By discovering hidden structures in models, establishing new analytical frameworks for complex systems, and promoting deep integration of fundamental research and clinical applications.