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1. Generalizing Graph ODE for Learning Complex System Dynamics across Environments

   https://doi.org/10.1145/3580305.3599362  

   Huang, Zijie; Sun, Yizhou; Wang, Wei (August 2023, Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’23))

   Learning multi-agent system dynamics has been extensively studied for various real-world applications, such as molecular dynamics in biology, multi-body system in physics, and particle dynamics in material science. Most of the existing models are built to learn single system dynamics, which learn the dynamics from observed historical data and predict the future trajectory. In practice, however, we might observe multiple systems that are generated across different environments, which differ in latent exogenous factors such as temperature and gravity. One simple solution is to learn multiple environment-specific models, but it fails to exploit the potential commonalities among the dynamics across environments and offers poor prediction results where per-environment data is sparse or limited. Here, we present GG-ODE (Generalized Graph Ordinary Differential Equations), a machine learning framework for learning continuous multi-agent system dynamics across environments. Our model learns system dynamics using neural ordinary differential equations (ODE) parameterized by Graph Neural Networks (GNNs) to capture the continuous interaction among agents. We achieve the model generalization by assuming the dynamics across different environments are governed by common physics laws that can be captured via learning a shared ODE function. The distinct latent exogenous factors learned for each environment are incorporated into the ODE function to account for their differences. To improve model performance, we additionally design two regularization losses to (1) enforce the orthogonality between the learned initial states and exogenous factors via mutual information minimization; and (2) reduce the temporal variance of learned exogenous factors within the same system via contrastive learning. Experiments over various physical simulations show that our model can accurately predict system dynamics, especially in the long range, and can generalize well to new systems with few observations. 

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2. S4S: Solving for a Diffusion Model Solver

   Frankel, E; Chen, S; Li, J; Koh, P W; Ratliff, L J; Oh, S (February 2025, https://doi.org/10.48550/arXiv.2502.17423)

   Diffusion models (DMs) create samples from a data distribution by starting from random noise and iteratively solving a reverse-time ordinary differential equation (ODE). Because each step in the iterative solution requires an expensive neural function evaluation (NFE), there has been significant interest in approximately solving these diffusion ODEs with only a few NFEs without modifying the underlying model. However, in the few NFE regime, we observe that tracking the true ODE evolution is fundamentally impossible using traditional ODE solvers. In this work, we propose a new method that learns a good solver for the DM, which we call Solving for the Solver (S4S). S4S directly optimizes a solver to obtain good generation quality by learning to match the output of a strong teacher solver. We evaluate S4S on six different pre-trained DMs, including pixel-space and latent-space DMs for both conditional and unconditional sampling. In all settings, S4S uniformly improves the sample quality relative to traditional ODE solvers. Moreover, our method is lightweight, data-free, and can be plugged in black-box on top of any discretization schedule or architecture to improve performance. Building on top of this, we also propose S4S-Alt, which optimizes both the solver and the discretization schedule. By exploiting the full design space of DM solvers, with 5 NFEs, we achieve an FID of 3.73 on CIFAR10 and 13.26 on MS-COCO, representing a 1.5× improvement over previous training-free ODE methods. 

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3. Task-Space Control of Continuum Robots using Underactuated Discrete Rod Models

   Caleb Rucker, Eric J. (October 2022, Proceedings of the IEEERSJ International Conference on Intelligent Robots and Systems)

   Underactuation is a core challenge associated with controlling soft and continuum robots, which possess theoretically infinite degrees of freedom, but few actuators. However, m actuators may still be used to control a dynamic soft robot in an m-dimensional output task space. In this paper we develop a task-space control approach for planar continuum robots that is robust to modeling error and requires very little sensor information. The controller is based on a highly underactuated discrete rod mechanics model in maximal coordinates and does not require conversion to a classical robot dynamics model form. This promotes straightforward control design, implementation and efficiency. We perform input-output feedback linearization on this model, apply sliding mode control to increase robustness, and formulate an observer to estimate the full state from sparse output measurements. Simulation results show exact task-space reference tracking behavior can be achieved even in the presence of significant modeling error, inaccurate initial conditions, and output-only sensing. 

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4. Physics-lumped parameter based control oriented model of dielectric tubular actuator

   https://doi.org/10.1007/s41315-021-00211-1  

   Kaaya, T; Wang, S; Cescon, M; Chen, Z (October 2021, International journal of intelligent robotics and applications)

   Dielectric elastomers (DEs) deform and change shape when an electric field is applied across them. They are flexible, resilient, lightweight, and durable and as such are suitable for use as soft actuators. In this paper a physics-based and control-oriented model is developed for a DE tubular actuator using a physics-lumped parameter modeling approach. The model derives from the nonlinear partial differential equations (PDE) which govern the nonlinear elasticity of the DE actuator and the ordinary differential equation (ODE) that governs the electrical dynamics of the DE actuator. With the boundary conditions for the tubular actuator, the nonlinear PDEs are numerically solved and a quasi-static nonlinear model is obtained and validated by experiments. The full nonlinear model is then linearized around an operating point with an analytically derived Hessian matrix. The analytically linearized model is validated by experiments. Proportional–Integral–Derivative (PID) and H∞ control are developed and implemented to perform position reference tracking of the DEA and the controllers’ performances are evaluated according to control energy and tracking error. 

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5. Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

   https://doi.org/10.1186/s12915-021-01115-z  

   Sego, T. J.; Aponte-Serrano, Josua O.; Gianlupi, Juliano F.; Glazier, James A. (September 2021, BMC Biology)

   Abstract BackgroundThe biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems. ResultsIn this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models. ConclusionWe developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes. 

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