相关论文: FNODE: Flow-Matching for data-driven simulation of…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…

Flow matching (FM) is increasingly used in scientific domains for time series generation and forecasting, where data often arise from underlying dynamical systems. However, it is not well-understood whether it learns transferable dynamical…

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. These models often require solving a system…

Learning-based planners are sensitive to the long-tailed distribution of driving data. Common maneuvers dominate datasets, while dangerous or rare scenarios are sparse. This imbalance can bias models toward the frequent cases and degrade…

Centralized trajectory optimization in the joint space of multiple robots allows access to a larger feasible space that can result in smoother trajectories, especially while planning in tight spaces. Unfortunately, it is often…

Continuous-time generative models, such as Flow Matching (FM), construct probability paths to transport between one distribution and another through the simulation-free learning of the neural ordinary differential equations (ODEs). During…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by…

Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions $p_t$. We identify a geometric optimization bottleneck in this regression problem: when the covariance $\Sigma_t$ of $p_t$ is…

With the increasing data volume, there is a trend of using large-scale pre-trained models to store the knowledge into an enormous number of model parameters. The training of these models is composed of lots of dense algebras, requiring a…

The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With the recent success of deep learning, there is increasing…

We develop a novel data-driven framework as an alternative to dynamic flux balance analysis, bypassing the demand for deep domain knowledge and manual efforts to formulate the optimization problem. The proposed framework is end-to-end,…

Fast and accurate simulation of dynamical systems is a fundamental challenge across scientific and engineering domains. Traditional numerical integrators often face a trade-off between accuracy and computational efficiency, while existing…

State estimation is important for a variety of tasks, from forecasting to substituting for unmeasured states in feedback controllers. Performing real-time state estimation for PDEs using provably and rapidly converging observers, such as…

Recent work by Xia et al. leveraged the continuous-limit of the classical momentum accelerated gradient descent and proposed heavy-ball neural ODEs. While this model offers computational efficiency and high utility over vanilla neural ODEs,…

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical…

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…