相关论文: Latent Generative Solvers for Generalizable Long-T…

The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…

When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…

Many astrophysical systems can only be accurately modelled when the behaviour of their baryonic gas components is well understood. The residual distribution (RD) family of partial differential equation (PDE) solvers produce approximate…

Deep generative models such as GANs, normalizing flows, and diffusion models are powerful regularizers for inverse problems. They exhibit great potential for helping reduce ill-posedness and attain high-quality results. However, the latent…

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models…

Generative Adversarial Networks (GANs) have achieved remarkable results in the task of generating realistic natural images. In most successful applications, GAN models share two common aspects: solving a challenging saddle point…

Probabilistic graphical models are traditionally known for their successes in generative modeling. In this work, we advocate layered graphical models (LGMs) for probabilistic discriminative learning. To this end, we design LGMs in close…

Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete…

Modeling the time-dependent evolution of electron density is essential for understanding quantum mechanical behaviors of condensed matter and enabling predictive simulations in spectroscopy, photochemistry, and ultrafast science. Yet, while…

Generative adversarial networks (GANs) were initially proposed to generate images by learning from a large number of samples. Recently, GANs have been used to emulate complex physical systems such as turbulent flows. However, a critical…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the…

Neural solvers for partial differential equations (PDEs) have great potential to generate fast and accurate physics solutions, yet their practicality is currently limited by their generalizability. PDEs evolve over broad scales and exhibit…

Training neural networks with high certified accuracy against adversarial examples remains an open challenge despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation,…

Latent-based image generative models, such as Latent Diffusion Models (LDMs) and Mask Image Models (MIMs), have achieved notable success in image generation tasks. These models typically leverage reconstructive autoencoders like VQGAN or…

Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the…

Large climate-model ensembles are computationally expensive; yet many downstream analyses would benefit from additional, statistically consistent realizations of spatiotemporal climate variables. We study a generative modeling approach for…

We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…

This paper introduces a novel method for numerically stabilizing sequential continuous adjoint flow solvers utilizing an elliptic relaxation strategy. The proposed approach is formulated as a Partial Differential Equation (PDE) containing a…

The ability to generate physically plausible ensembles of variable sources is critical to the optimization of time-domain survey cadences and the training of classification models on datasets with few to no labels. Traditional data…