Ruikun Li

Ruikun Li, Huandong Wang, Jingtao Ding et al.

Data-driven dynamics prediction often fails under environmental shifts, while traditional fine-tuning remains computationally prohibitive for hardware-constrained or data-scarce applications. We propose DynaDiff, a generative meta-learning framework that transitions the paradigm from gradient-based tuning or modulation to direct weight-space generation. Specifically, we first abstract expert weights as novel weight graphs, utilizing multi-head attention to explicitly capture topological coupling within weights. Subsequently, we design a functional loss to ensure that the generated models achieve consistency with expert models in physical behavior. Finally, we develop a dynamics-informed prompter that extracts cross-domain physical and spectral features from observation sequences to condition the diffusion model. Experiments demonstrate that DynaDiff boosts average prediction accuracy by 10.78% over competitive baselines. Furthermore, by pre-constructing a model zoo of expert predictors, we amortize the fine-tuning overhead into a one-time offline cost, significantly boosting deployment efficiency in new environments.

Ruikun Li, Huandong Wang, Qingmin Liao et al.

Energy landscapes play a crucial role in shaping dynamics of many real-world complex systems. System evolution is often modeled as particles moving on a landscape under the combined effect of energy-driven drift and noise-induced diffusion, where the energy governs the long-term motion of the particles. Estimating the energy landscape of a system has been a longstanding interdisciplinary challenge, hindered by the high operational costs or the difficulty of obtaining supervisory signals. Therefore, the question of how to infer the energy landscape in the absence of true energy values is critical. In this paper, we propose a physics-informed self-supervised learning method to learn the energy landscape from the evolution trajectories of the system. It first maps the system state from the observation space to a discrete landscape space by an adaptive codebook, and then explicitly integrates energy into the graph neural Fokker-Planck equation, enabling the joint learning of energy estimation and evolution prediction. Experimental results across interdisciplinary systems demonstrate that our estimated energy has a correlation coefficient above 0.9 with the ground truth, and evolution prediction accuracy exceeds the baseline by an average of 17.65\%. The code is available at github.com/tsinghua-fib-lab/PESLA.

Lequan Lin, Zhengkun Li, Ruikun Li et al.

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data, diffusion models are widely used in image, video, and text synthesis nowadays. In recent years, the concept of diffusion has been extended to time series applications, and many powerful models have been developed. Considering the deficiency of a methodical summary and discourse on these models, we provide this survey as an elementary resource for new researchers in this area and also an inspiration to motivate future research. For better understanding, we include an introduction about the basics of diffusion models. Except for this, we primarily focus on diffusion-based methods for time series forecasting, imputation, and generation, and present them respectively in three individual sections. We also compare different methods for the same application and highlight their connections if applicable. Lastly, we conclude the common limitation of diffusion-based methods and highlight potential future research directions.