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We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…
Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…
The sequential nature of autoregressive next-token prediction imposes a fundamental speed limit on large language models. While continuous flow models offer a path to parallel generation, they traditionally demand expensive iterative…
Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…
Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…
Simulating and predicting the water level/stage in river systems is essential for flood warnings, hydraulic operations, and flood mitigations. Physics-based detailed hydrological and hydraulic computational tools, such as HEC-RAS, MIKE, and…
Shallow water equations (SWEs) are the backbone of most hydrodynamics models for flood prediction, river engineering, and many other water resources applications. The estimation of flow resistance, i.e., the Manning's roughness coefficient…
Quantum reservoir computing has emerged as a promising paradigm for harnessing quantum systems to process temporal data efficiently by bypassing the costly training of gradient-based learning methods. Here, we demonstrate the capability of…
Diffusion-based models on continuous spaces have seen substantial recent progress through the mathematical framework of gradient flows, leveraging the Wasserstein-2 (${W}_2$) metric via the Jordan-Kinderlehrer-Otto (JKO) scheme. Despite the…
This paper introduces Gauge Flow Models, a novel class of Generative Flow Models. These models incorporate a learnable Gauge Field within the Flow Ordinary Differential Equation (ODE). A comprehensive mathematical framework for these…
The coordination of cascading hydropower systems represents a fundamental challenge in modern energy systems engineering, requiring a sophisticated balance between multi-reservoir physics, stringent environmental regulations, and dynamic…
A first differentiable analysis pipeline is presented for an example high-energy physics (HEP) use case with publicly available collision data from the Compact Muon Solenoid detector at the Large Hadron Collider. The pipeline combines tools…
Extracting information on fluid motion directly from images is challenging. Fluid flow represents a complex dynamic system governed by the Navier-Stokes equations. General optical flow methods are typically designed for rigid body motion,…
Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…
Data-driven hourly weather forecasting models often face the challenge of error accumulation in long-term predictions. The problem is exacerbated by non-physical temporal discontinuities present in widely-used training datasets such as…
Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key challenge is to design linear layers that enhance expressiveness while maintaining efficient…
Statistical modeling of monthly, seasonal, or annual rainfall data is an important research area in meteorology. These models play a crucial role in rainfed agriculture, where a proper assessment of the future availability of rainwater is…
Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models and developing novel models, relatively limited…
We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…
Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…