FlowDAS: A Flow-Based Framework for Data Assimilation
- URL: http://arxiv.org/abs/2501.16642v1
- Date: Mon, 13 Jan 2025 05:03:41 GMT
- Title: FlowDAS: A Flow-Based Framework for Data Assimilation
- Authors: Siyi Chen, Yixuan Jia, Qing Qu, He Sun, Jeffrey A Fessler,
- Abstract summary: FlowDAS is a novel generative model-based framework using the interpolants to unify the learning of state transition dynamics and generative priors.<n>Our experiments demonstrate FlowDAS's superior performance on various benchmarks, from the Lorenz system to high-dimensional fluid superresolution tasks.
- Score: 15.64941169350615
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Data assimilation (DA) is crucial for improving the accuracy of state estimation in complex dynamical systems by integrating observational data with physical models. Traditional solutions rely on either pure model-driven approaches, such as Bayesian filters that struggle with nonlinearity, or data-driven methods using deep learning priors, which often lack generalizability and physical interpretability. Recently, score-based DA methods have been introduced, focusing on learning prior distributions but neglecting explicit state transition dynamics, leading to limited accuracy improvements. To tackle the challenge, we introduce FlowDAS, a novel generative model-based framework using the stochastic interpolants to unify the learning of state transition dynamics and generative priors. FlowDAS achieves stable and observation-consistent inference by initializing from proximal previous states, mitigating the instability seen in score-based methods. Our extensive experiments demonstrate FlowDAS's superior performance on various benchmarks, from the Lorenz system to high-dimensional fluid super-resolution tasks. FlowDAS also demonstrates improved tracking accuracy on practical Particle Image Velocimetry (PIV) task, showcasing its effectiveness in complex flow field reconstruction.
Related papers
- PI-WAN: A Physics-Informed Wind-Adaptive Network for Quadrotor Dynamics Prediction in Unknown Environments [3.4802474792943805]
We introduce the Physics-Informed Wind-Adaptive Network (PI-WAN), which embeds physical constraints directly into the training process for robust quadrotor dynamics learning.<n>Specifically, PI-WAN employs a Temporal Convolutional Network (TCN) architecture that efficiently captures temporal dependencies from historical flight data.<n>By incorporating real-time prediction results into a model predictive control (MPC) framework, we achieve improvements in closed-loop tracking performance.
arXiv Detail & Related papers (2025-07-01T14:48:22Z) - Consistent World Models via Foresight Diffusion [56.45012929930605]
We argue that a key bottleneck in learning consistent diffusion-based world models lies in the suboptimal predictive ability.<n>We propose Foresight Diffusion (ForeDiff), a diffusion-based world modeling framework that enhances consistency by decoupling condition understanding from target denoising.
arXiv Detail & Related papers (2025-05-22T10:01:59Z) - Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models [71.63194926457119]
We introduce Dynamical Diffusion (DyDiff), a theoretically sound framework that incorporates temporally aware forward and reverse processes.
Experiments across scientifictemporal forecasting, video prediction, and time series forecasting demonstrate that Dynamical Diffusion consistently improves performance in temporal predictive tasks.
arXiv Detail & Related papers (2025-03-02T16:10:32Z) - Graph Neural Networks and Differential Equations: A hybrid approach for data assimilation of fluid flows [0.0]
This study presents a novel hybrid approach that combines Graph Neural Networks (GNNs) with Reynolds-Averaged Navier Stokes (RANS) equations.
The results demonstrate significant improvements in the accuracy of the reconstructed mean flow compared to purely data-driven models.
arXiv Detail & Related papers (2024-11-14T14:31:52Z) - FlowTS: Time Series Generation via Rectified Flow [67.41208519939626]
FlowTS is an ODE-based model that leverages rectified flow with straight-line transport in probability space.
For unconditional setting, FlowTS achieves state-of-the-art performance, with context FID scores of 0.019 and 0.011 on Stock and ETTh datasets.
For conditional setting, we have achieved superior performance in solar forecasting.
arXiv Detail & Related papers (2024-11-12T03:03:23Z) - On conditional diffusion models for PDE simulations [53.01911265639582]
We study score-based diffusion models for forecasting and assimilation of sparse observations.
We propose an autoregressive sampling approach that significantly improves performance in forecasting.
We also propose a new training strategy for conditional score-based models that achieves stable performance over a range of history lengths.
arXiv Detail & Related papers (2024-10-21T18:31:04Z) - Combined Optimization of Dynamics and Assimilation with End-to-End Learning on Sparse Observations [1.492574139257933]
CODA is an end-to-end optimization scheme for jointly learning dynamics and DA directly from sparse and noisy observations.
We introduce a novel learning objective that combines unrolled auto-regressive dynamics with the data- and self-consistency terms of weak-constraint 4Dvar DA.
arXiv Detail & Related papers (2024-09-11T09:36:15Z) - Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operator [0.0]
Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and the earth system.<n>For systems without a clear scale, generalization deterministic and local closure models often lack enough capability.<n>We propose a datadriven modeling framework for constructing neural operator and non-local closure models.
arXiv Detail & Related papers (2024-08-06T05:21:31Z) - Physics-guided Active Sample Reweighting for Urban Flow Prediction [75.24539704456791]
Urban flow prediction is a nuanced-temporal modeling that estimates the throughput of transportation services like buses, taxis and ride-driven models.
Some recent prediction solutions bring remedies with the notion of physics-guided machine learning (PGML)
We develop a atized physics-guided network (PN), and propose a data-aware framework Physics-guided Active Sample Reweighting (P-GASR)
arXiv Detail & Related papers (2024-07-18T15:44:23Z) - PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction [5.06136344261226]
CNN-based methods for data fidelity enhancement rely on low-fidelity data patterns and distributions during the training phase.
Our proposed model - Physics-informed Residual Diffusion - demonstrates the capability to elevate the quality of data from both standard low-fidelity inputs.
Experimental results have shown that our approach can effectively reconstruct high-quality outcomes for two-dimensional turbulent flows without requiring retraining.
arXiv Detail & Related papers (2024-04-12T11:45:51Z) - Guided Flows for Generative Modeling and Decision Making [55.42634941614435]
We show that Guided Flows significantly improves the sample quality in conditional image generation and zero-shot text synthesis-to-speech.
Notably, we are first to apply flow models for plan generation in the offline reinforcement learning setting ax speedup in compared to diffusion models.
arXiv Detail & Related papers (2023-11-22T15:07:59Z) - Generative Modeling with Phase Stochastic Bridges [49.4474628881673]
Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs.
We introduce a novel generative modeling framework grounded in textbfphase space dynamics
Our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.
arXiv Detail & Related papers (2023-10-11T18:38:28Z) - Diffusion Generative Flow Samplers: Improving learning signals through
partial trajectory optimization [87.21285093582446]
Diffusion Generative Flow Samplers (DGFS) is a sampling-based framework where the learning process can be tractably broken down into short partial trajectory segments.
Our method takes inspiration from the theory developed for generative flow networks (GFlowNets)
arXiv Detail & Related papers (2023-10-04T09:39:05Z) - Data-driven Modeling and Inference for Bayesian Gaussian Process ODEs
via Double Normalizing Flows [28.62579476863723]
We introduce normalizing flows to re parameterize the ODE vector field, resulting in a data-driven prior distribution.
We also apply normalizing flows to the posterior inference of GP ODEs to resolve the issue of strong mean-field assumptions.
We validate the effectiveness of our approach on simulated dynamical systems and real-world human motion data.
arXiv Detail & Related papers (2023-09-17T09:28:47Z) - Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation [26.520247496906492]
In this work, we analyze if fully data-driven fluid solvers that utilize an autoregressive rollout based on conditional diffusion models are a viable option to address this challenge.<n>To quantitatively and qualitatively benchmark the performance of various flow prediction approaches, three challenging 2D scenarios including incompressible and transonic flows, as well as isotropic turbulence are employed.<n>We find that even simple diffusion-based approaches can outperform multiple established flow prediction methods in terms of accuracy and temporal stability, while being on par with state-of-the-art stabilization techniques like unrolling at training time.
arXiv Detail & Related papers (2023-09-04T18:01:42Z) - Learning continuous models for continuous physics [94.42705784823997]
We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications.
Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
arXiv Detail & Related papers (2022-02-17T07:56:46Z) - Autoregressive Dynamics Models for Offline Policy Evaluation and
Optimization [60.73540999409032]
We show that expressive autoregressive dynamics models generate different dimensions of the next state and reward sequentially conditioned on previous dimensions.
We also show that autoregressive dynamics models are useful for offline policy optimization by serving as a way to enrich the replay buffer.
arXiv Detail & Related papers (2021-04-28T16:48:44Z) - Training Deep Normalizing Flow Models in Highly Incomplete Data
Scenarios with Prior Regularization [13.985534521589257]
We propose a novel framework to facilitate the learning of data distributions in high paucity scenarios.
The proposed framework naturally stems from posing the process of learning from incomplete data as a joint optimization task.
arXiv Detail & Related papers (2021-04-03T20:57:57Z) - Stochastically forced ensemble dynamic mode decomposition for
forecasting and analysis of near-periodic systems [65.44033635330604]
We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system.
We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony.
Results are presented for a test case using load data from an electrical grid.
arXiv Detail & Related papers (2020-10-08T20:25:52Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.