Related papers: DICE: Discrete inverse continuity equation for lea…

A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…

The abundance of data affords researchers to pursue more powerful computational tools to learn the dynamics of complex system, such as neural networks, engineered systems and social networks. Traditional machine learning approaches capture…

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

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…

The score function estimator is widely used for estimating gradients of stochastic objectives in stochastic computation graphs (SCG), eg, in reinforcement learning and meta-learning. While deriving the first-order gradient estimators by…

We propose a physics-aware Consistency Training (CT) method that accelerates sampling in Diffusion Models with physical constraints. Our approach leverages a two-stage strategy: (1) learning the noise-to-data mapping via CT, and (2)…

Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a…

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

We address the problem of predicting the next state of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural black-box solution to…

We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…

We propose Speech Enhancement based on Drifting Models (DriftSE), a novel generative framework that formulates denoising as an equilibrium problem. Rather than relying on iterative sampling, DriftSE natively achieves one-step inference by…

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…

Modern robotics is gravitating toward increasingly collaborative human robot interaction. Tools such as acceleration policies can naturally support the realization of reactive, adaptive, and compliant robots. These tools require us to model…

The recent proliferation of diffusion models has made style mimicry effortless, enabling users to imitate unique artistic styles without authorization. In deployed platforms, this raises copyright and intellectual-property risks and calls…

Oftentimes, environments for sequential decision-making problems can be quite sparse in the provision of evaluative feedback to guide reinforcement-learning agents. In the extreme case, long trajectories of behavior are merely punctuated…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

One of the widely used models for studying economics of climate change is the Dynamic Integrated model of Climate and Economy (DICE), which has been developed by Professor William Nordhaus, one of the laureates of the 2018 Nobel Memorial…

Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…

This paper introduces two variational inference approaches for infinite-dimensional inverse problems, developed through gradient descent with a constant learning rate. The proposed methods enable efficient approximate sampling from the…