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Related papers: PINF: Continuous Normalizing Flows for Physics-Con…

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Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…

Machine Learning · Statistics 2021-11-15 Brendan Leigh Ross , Jesse C. Cresswell

Physics-Informed Neural Networks (PINNs) integrate physical principles into machine learning, finding wide applications in various science and engineering fields. However, solving nonlinear hyperbolic partial differential equations (PDEs)…

Fluid Dynamics · Physics 2024-10-01 Jingjing Zhang , Ulisses Braga-Neto , Eduardo Gildin

Many conservative physical systems can be described using the Hamiltonian formalism. A notable example is the Vlasov-Poisson equations, a set of partial differential equations that govern the time evolution of a phase-space density function…

Machine Learning · Computer Science 2025-05-09 Vincent Souveton , Sébastien Terrana

Real-time, physically-consistent predictions on low-power edge devices is critical for the next generation embodied AI systems, yet it remains a major challenge. Physics-Informed Neural Networks (PINNs) combine data-driven learning with…

Machine Learning · Computer Science 2025-12-01 Chi Zhang , Lin Wang

Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…

Machine Learning · Computer Science 2024-04-25 Felix Draxler , Peter Sorrenson , Lea Zimmermann , Armand Rousselot , Ullrich Köthe

Model discovery aims at autonomously discovering differential equations underlying a dataset. Approaches based on Physics Informed Neural Networks (PINNs) have shown great promise, but a fully-differentiable model which explicitly learns…

Machine Learning · Statistics 2021-10-06 Gert-Jan Both , Remy Kusters

The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution…

Computational Physics · Physics 2021-10-25 Bo Lin , Qianxiao Li , Weiqing Ren

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…

Machine Learning · Computer Science 2024-04-05 Zakaria Elabid , Daniel Busby , Abdenour Hadid

We present zephyr, a novel method that integrates cutting-edge normalizing flow techniques into a mixture density estimation framework, enabling the effective use of heterogeneous training data for photometric redshift inference. Compared…

Instrumentation and Methods for Astrophysics · Physics 2023-11-01 Zechang Sun , Joshua S. Speagle , Song Huang , Yuan-Sen Ting , Zheng Cai

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs) by directly embedding them into the loss function. Despite their notable success, existing PINNs often exhibit training…

Computational Engineering, Finance, and Science · Computer Science 2026-03-26 Chang Wei , Yuchen Fan , Chin Chun Ooi , Jian Cheng Wong , Heyang Wang , Pao-Hsiung Chiu

Deep learning method has attracted tremendous attention to handle fluid dynamics in recent years. However, the deep learning method requires much data to guarantee the generalization ability and the data of fluid dynamics are deficient.…

Fluid Dynamics · Physics 2021-11-18 Guang-Tao Zhang , Chen Cheng , Shu-dong Liu , Yang Chen , Yong-Zheng Li

Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations…

Machine Learning · Computer Science 2023-09-11 Keegan Kelly , Lorena Piedras , Sukrit Rao , David Roth

Physics-Informed Neural Networks (PINNs) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard…

Numerical Analysis · Mathematics 2026-01-19 Ahmed Aberqi , Ahmed Miloudi

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise.…

Machine Learning · Computer Science 2024-06-28 Peter Sorrenson , Felix Draxler , Armand Rousselot , Sander Hummerich , Lea Zimmermann , Ullrich Köthe

In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes…

Machine Learning · Statistics 2022-04-05 Elouan Argouarc'h , François Desbouvries , Eric Barat , Eiji Kawasaki , Thomas Dautremer

This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the…

Mathematical Physics · Physics 2022-05-03 S. Katagiri , Y. Matsuo , Y. Matsuoka , A. Sugamoto

Machine Learning (ML) models in Robotic Assembly Sequence Planning (RASP) need to be introspective on the predicted solutions, i.e. whether they are feasible or not, to circumvent potential efficiency degradation. Previous works need both…

The Fokker-Planck (FP) equation governs the evolution of densities for stochastic dynamics of physical systems, such as the Langevin dynamics and the Lorenz system. This work simulates FP equations through a mean field control (MFC)…

Optimization and Control · Mathematics 2025-08-06 Mo Zhou , Stanley Osher , Wuchen Li

Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by…

Machine Learning · Computer Science 2021-07-14 Ruizhi Deng , Bo Chang , Marcus A. Brubaker , Greg Mori , Andreas Lehrmann

Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…

Numerical Analysis · Mathematics 2025-12-23 Yang Zhao , Haoyu Lu , Junxiong Jia , Tao Zhou