Health Data Science CDT

该项目属于EPSRC人工智能和机器人研究领域的福尔斯。当前的生成模型虽然在各种应用中具有鲁棒性，但难以表示生物和化学系统的多种复杂性和瞬态动力学。这在生物医学应用中尤其明显，例如单细胞RNA测序，其中横截面样品的破坏性性质需要从静态稀疏数据点推断细胞动力学[1]。类似地，在生物化学中，化学反应中瞬态的模拟仅限于物理上合理的路径，而不是简单的直线轨迹[2]。该项目提出了新的生成建模框架的开发，将几何学习和物理定律直接集成到模型架构中。预期的结果是更有效的生成模型，用于理解生物医学研究和化学中的动态系统，更好地反映（从而理解）这些系统的潜在动力学并加速模拟。几何模型我们提出了一种称为度量流匹配（MFM）的方法[3]-一种为轨迹推断而设计的新颖生成框架。它利用数据诱导的黎曼度量来学习近似测地线。通过采用测地线路径，MFM更紧密地遵循数据的底层几何结构，并在预测单细胞轨迹方面展示了最先进的性能。对MFM的进一步改进可以提高单细胞轨迹编码任务特定偏差的模型特异性和准确性[4]，通过结合最佳运输计划解决数据不平衡问题，或者通过设计具有热内核的运输计划来改进无模拟耦合以尊重流形假设。物理信息我们的下一个目标是集成物理约束（例如，Langevin动力学[5]）以增强分子跃迁路径采样[2]、分子动力学[6]或对接[7]。这些约束可以类似于MFM被纳入生成模型中，用物理偏差代替几何偏差，类似于在物理信息神经网络和神经运算符中探索的方法，而不是在MFM中提出的几何偏差。例如，在分子动力学中，确保这些动力学的平衡条件特征被保留，沿着相应的福克-普朗克方程，有可能显着加快化学模拟，如[6]最初提出的。此外，通过设计合适的偏置，这些模型还可以改善对玻尔兹曼型能量所指示的复杂分布的完全覆盖的捕获[8]。参考文献[1] Laundry，Hugo等人，“Towards a mathematical theory of trajectory inference.“arXiv预印本arXiv：2102.09204（2021）[2] Holdijk，Lars，et al.“Stochastic optimal control for collective variable free sampling of molecular transition paths.神经信息处理系统的进展36（2024）。[3]Kapusniak，Kacper等人，“数据流形上平滑插值的度量流匹配。arXiv预印本arXiv：2405.14780（2024）。[4]Neklyudov，Kirill等人，“解决Wasserstein拉格朗日流的计算框架。arXiv预印本arXiv：2310.10649（2023）。[5]布西，乔瓦尼，和米歇尔帕里内洛。“使用朗之万动力学进行精确采样。物理评论E-Statistical，Nonlinear，and Soft Matter Physics 75.5（2007）：056707. [6]Klein，Leon等人，“Timewarp：通过学习时间粗化动力学来实现分子动力学的可转移加速。神经信息处理系统的进展36（2024）。[7]Corso，Gabriele等人，“Diffdock：分子对接的扩散步骤、扭曲和转折。arXiv预印本arXiv：2210.01776（2022）。[8]Akhound-Sadegh，塔拉等人，“从玻尔兹曼密度采样的迭代去噪能量匹配。arXiv预印本arXiv：2402.06121（2024）。

This project falls within the EPSRC Artificial Intelligence and Robotics research area.Current generative models, while robust in various applications, struggle to represent the manifold complexities and transient dynamics of biological and chemical systems. This is particularly evident in biomedical applications, such as single-cell RNA sequencing, where the destructive nature of cross-sectional samples necessitates the inference of cell dynamics from static, sparse data points [1]. Similarly, in biochemistry, the simulation of transient states in chemical reactions is limited to physically plausible paths beyond simple straight-line trajectories [2].This project proposes the development of novel generative modeling frameworks that integrate geometric learning and physical laws directly into the model architecture. The expected outcome is more effective generative models for understanding dynamic systems in biomedical research and chemistry, better reflecting (and thus understanding) the underlying dynamics of these systems and speeding up simulations.Geometric ModelsWe propose a method called Metric Flow Matching (MFM) [3]-a novel generative framework designed for trajectory inference. It utilizes data- induced Riemannian metrics to learn approximate geodesics. By adopting geodesic paths, MFM adheres more closely to the data's underlying geometry and demonstrates state-of-the-art performance in predicting single-cell trajectories.Further improvements to MFM could enhance model specificity and accuracy for single-cell trajectories-encoding task-specific biases [4], addressing data imbalance by incorporating optimal transport plans, or refining simulation-free couplings to respect the manifold assumption by designing transport plan with heat kernels.Physics-InformedOur next objective is integrating physical constraints (e.g., Langevin dynamics [5]) to enhance molecular transition path sampling [2], Molecular Dynamics [6], or Docking [7]. These constraints could be incorporated into generative models similarly to MFM, replacing geometric bias with physical ones, akin to methods explored in Physics-Informed Neural Networks and Neural Operators instead of Geometric Metrics proposed in MFM.For instance, in Molecular Dynamics, ensuring balanced conditions characteristic of these dynamics are preserved, along with the corresponding Fokker-Planck equation, has the potential to significantly speed up chemical simulations, as initially presented by [6]. Furthermore,by designing suitable biases, these models could also improve capturing the full coverage of complex distributions dictated by Boltzmann-type energies [8].References[1] Lavenant, Hugo, et al. "Towards a mathematical theory of trajectory inference." arXiv preprint arXiv:2102.09204 (2021)[2] Holdijk, Lars, et al. "Stochastic optimal control for collective variable free sampling of molecular transition paths." Advances in Neural Information Processing Systems 36 (2024).[3] Kapusniak, Kacper, et al. "Metric Flow Matching for Smooth Interpolations on the Data Manifold." arXiv preprint arXiv:2405.14780 (2024).[4] Neklyudov, Kirill, et al. "A computational framework for solving Wasserstein Lagrangian flows." arXiv preprint arXiv:2310.10649 (2023).[5] Bussi, Giovanni, and Michele Parrinello. "Accurate sampling using Langevin dynamics." Physical Review E-Statistical, Nonlinear, and Soft Matter Physics 75.5 (2007): 056707.[6] Klein, Leon, et al. "Timewarp: Transferable acceleration of molecular dynamics by learning time-coarsened dynamics." Advances in Neural Information Processing Systems 36 (2024).[7] Corso, Gabriele, et al. "Diffdock: Diffusion steps, twists, and turns for molecular docking." arXiv preprint arXiv:2210.01776(2022).[8] Akhound-Sadegh, Tara, et al. "Iterated denoising energy matching for sampling from Boltzmann densities." arXiv preprint arXiv:2402.06121 (2024).