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PDE-Driven Spatiotemporal Disentanglement [article]

Jérémie Donà
2021 arXiv   pre-print
This inspiration allows us to introduce a dynamical interpretation of spatiotemporal disentanglement.  ...  It induces a principled model based on learning disentangled spatial and temporal representations of a phenomenon to accurately predict future observations.  ...  EXPERIMENTS PHYSICAL DATASETS: WAVE EQUATION AND SEA SURFACE TEMPERATURE We first investigate two synthetic dynamical systems and a real-world dataset in order to show the advantage of PDE-driven spatiotemporal  ... 
arXiv:2008.01352v3 fatcat:di3nuh7jcnggdm2px44hiukb4m

Embedding Physics to Learn Spatiotemporal Dynamics from Sparse Data [article]

Chengping Rao, Hao Sun, Yang Liu
2021 arXiv   pre-print
dynamics in a data-driven manner.  ...  Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs) that are typically derived from first principles.  ...  ., physical cell and ConvLSTM cell in parallel, to disentangle the dynamics of a spatiotemporal systems.  ... 
arXiv:2106.04781v1 fatcat:j3kacxwmerbhpeklrveqhw6jb4

Extracting Interpretable Physical Parameters from Spatiotemporal Systems using Unsupervised Learning [article]

Peter Y. Lu, Samuel Kim, Marin Soljačić
2019 arXiv   pre-print
variables that alter the system dynamics and cause varying behaviors that are difficult to disentangle.  ...  For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics.  ...  The ultimate goal of this work is to provide additional insight into complex spatiotemporal dynamics using a data-driven approach.  ... 
arXiv:1907.06011v2 fatcat:a6r25xyk2nhqvamqgo3mwlkwqy

Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning [article]

Chengping Rao, Pu Ren, Yang Liu, Hao Sun
2022 arXiv   pre-print
To overcome this challenge, we propose a novel physics-encoded discrete learning framework for discovering spatiotemporal PDEs from scarce and noisy data.  ...  Although past research attempts have achieved great success in data-driven PDE discovery, the robustness of the existing methods cannot be guaranteed when dealing with low-quality measurement data.  ...  Data-driven discovery. The data-driven discovery is also a renascent research attempt.  ... 
arXiv:2201.12354v1 fatcat:lks4nimsxfbcvc7522l4ob7opu

When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning [article]

Chuizheng Meng, Sungyong Seo, Defu Cao, Sam Griesemer, Yan Liu
2022 arXiv   pre-print
Physics-informed machine learning (PIML), referring to the combination of prior knowledge of physics, which is the high level abstraction of natural phenomenons and human behaviours in the long history, with data-driven  ...  deep learning and model-driven computation for reliable spatiotemporal evolution prediction.  ...  Recently, PhyDNet [104] explicitly disentangles PDE dynamics from unknown complementary information.  ... 
arXiv:2203.16797v1 fatcat:zfynhlkcerfkvizlsftffr4g6a

wav2shape: Hearing the Shape of a Drum Machine [article]

Han Han, Vincent Lostanlen
2020 arXiv   pre-print
Disentangling and recovering physical attributes, such as shape and material, from a few waveform examples is a challenging inverse problem in audio signal processing, with numerous applications in musical  ...  Once in the Laplace-SLT domain, the solution of the PDE can be recovered in the spatiotemporal domain by performing an inverse Sturm-Liouville and inverse Laplace transform consecutively.  ...  In this context, we believe that future research is needed to strengthen the interoperability between physical modeling and data-driven modeling of musical sounds.  ... 
arXiv:2007.10299v1 fatcat:vpcabpavpbbhnbid24lc72py7u

Physics-Guided Deep Learning for Dynamical Systems: A Survey [article]

Rui Wang, Rose Yu
2022 arXiv   pre-print
dynamics forecasting that performs spatiotemporal disentanglement using the functional variable separation.  ...  Many questions remain open, such as using causality to improve DL models and disentangling complex and multiple treatments.  ... 
arXiv:2107.01272v5 fatcat:k6hhdt6csnfebgkzrpuoeqkwzi

Unsupervised physics-informed disentanglement of multimodal data for high-throughput scientific discovery [article]

Nathaniel Trask, Carianne Martinez, Kookjin Lee, Brad Boyce
2022 arXiv   pre-print
Sampling from clusters allows cross-modal generative modeling, with a mixture of expert decoder imposing inductive biases encoding prior scientific knowledge and imparting structured disentanglement of  ...  Disentanglement Another line of research is to extract latent disentangled representations into different factors of variations in data using VAEs.  ...  Accordingly, we aim to discover comprehensive fingerprints constructed from the weighted integration of several disparate data sources, each with unique fidelity, sparsity, and spatiotemporal resolution  ... 
arXiv:2202.03242v1 fatcat:2mox3xydzrfqhac5kasdxrf7ci

Applications of physics-informed scientific machine learning in subsurface science: A survey [article]

Alexander Y. Sun, Hongkyu Yoon, Chung-Yan Shih, Zhi Zhong
2021 arXiv   pre-print
The main difference is that additional PDE loss terms related to the PDE being solved are incorporated.  ...  For example, spatiotemporal graph convolution network (ST-GCN) and spatiotemporal multi-graph convolution network [Geng et al., 2019] were used for skeleton-based action recognition and for ride share  ... 
arXiv:2104.04764v2 fatcat:h2vx3gn2snc6th23x5bylahy6i

CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations [article]

Peter Yichen Chen, Jinxu Xiang, Dong Heon Cho, G A Pershing, Henrique Teles Maia, Maurizio Chiaramonte, Kevin Carlberg, Eitan Grinspun
2022 arXiv   pre-print
We propose to accelerate PDE solvers using reduced-order modeling (ROM).  ...  After the low-dimensional manifolds are built, solving PDEs requires significantly less computational resources.  ...  After the manifold is built, we solve the PDEs by computing latent space dynamics.  ... 
arXiv:2206.02607v1 fatcat:sdquradqdfhoxcj3ok6vwxtxpe

Deep-learning-based prediction of nanoparticle phase transitions during in situ transmission electron microscopy [article]

Wenkai Fu, Steven R. Spurgeon, Chongmin Wang, Yuyan Shao, Wei Wang, Amra Peles
2022 arXiv   pre-print
The physical dynamics are captured by PhyCell, which models a generic class of linear PDEs. The unphysical factors are simulated by the data-driven convLSTM.  ...  The two-branch architecture of PhyCell and convLSTM in PhyDNet were designed to disentangle physical dynamics that can be described by partial differential equations (PDEs) from unphysical factors [6]  ... 
arXiv:2205.11407v1 fatcat:d76jp4wklnatpatxky5c5qprea

Questionnaires to PDEs: From Disorganized Data to Emergent Generative Dynamic Models [article]

David W. Sroczynski, Felix P. Kemeth, Ronald R. Coifman, Ioannis G. Kevrekidis
2022 arXiv   pre-print
of parameter dependent, evolutionary partial differential equation (PDE) models capable of generating the data.  ...  This allows us to discuss features of the process like symmetry breaking, translational invariance, and autonomousness of the emergent PDE model, as well as its interpretability.  ...  Without any of the myriad details, the point is that one could try and "learn" an evolution PDE for this spatiotemporal signal from the data.  ... 
arXiv:2204.11961v1 fatcat:hh7qjeniebgwpbgxjkazntzqly

Review and perspective on mathematical modeling of microbial ecosystems

Antonella Succurro, Oliver Ebenhöh
2018 Biochemical Society Transactions  
An ecosystem is a complex network of dynamic spatiotemporal interactions among organisms as well as between organisms and the environment.  ...  system of five PDEs and four ODEs.  ...  [35] recently proposed an effective strategy for a data-driven network reconstruction.  ... 
doi:10.1042/bst20170265 pmid:29540507 pmcid:PMC5906705 fatcat:elohppvrifcnxahhzl2jwuujaq

Isolating and Leveraging Controllable and Noncontrollable Visual Dynamics in World Models [article]

Minting Pan, Xiangming Zhu, Yunbo Wang, Xiaokang Yang
2022 arXiv   pre-print
First, by optimizing the inverse dynamics, we encourage the world model to learn controllable and noncontrollable sources of spatiotemporal changes on isolated state transition branches.  ...  PDE dynamics from unknown complementary information.  ...  Basic Assumptions of Iso-Dream As shown in Figure 1 , when the agent receives a sequence of visual observations o 1:T , the underlying spatiotemporal dynamics can be defined as u 1:T .  ... 
arXiv:2205.13817v1 fatcat:4rujsfsulvaibjowv6xyibf5xi

Deep Learning Models for Global Coordinate Transformations that Linearize PDEs [article]

Craig Gin, Bethany Lusch, Steven L. Brunton, J. Nathan Kutz
2019 arXiv   pre-print
We develop a deep autoencoder architecture that can be used to find a coordinate transformation which turns a nonlinear PDE into a linear PDE.  ...  Our architecture is motivated by the linearizing transformations provided by the Cole-Hopf transform for Burgers equation and the inverse scattering transform for completely integrable PDEs.  ...  Introduction Partial differential equations (PDEs) provide a theoretical framework for modeling spatiotemporal systems across the biological, physical and engineering sciences.  ... 
arXiv:1911.02710v1 fatcat:spxzjxfb3rfnbdsztmtra52vpu
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