We conclude the paper by discussing an agenda of research The idea of using neural network (NN) to intelligentize machines can be traced to 1942 when a simple model was proposed to simulate the status of a single neuron. Project+Code: https://ge.in.tum.de/publications/2020-iclr-holl/, Lagrangian Fluid Simulation with Continuous Convolutions , PDF: https://arxiv.org/pdf/1905.11075, phiflow: https://github.com/tum-pbs/phiflow, diff-taichi: https://github.com/yuanming-hu/difftaichi. In this paper, we have provided an overview of physical-layer deep learning and the state of the art in this topic. As a practical case study, the authors train several models to address the problem of modulation recognition. These FIRs compensate current channel conditions by being applied at the transmitter’s side. layer, and then summarize the current state of the art and existing PDF: https://arxiv.org/pdf/2003.14358, Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence , solve, and how tightly the physical model is integrated into the The newly-developed Platforms for Advanced Wireless Research (PAWR) will be fundamental in addressing the above challenge [pawr]. Learning-based Radio Fingerprinting Algorithms, Big Data Goes Small: Real-Time Spectrum-Driven Embedded Wireless This article provides an overview of the recent advancements in DL-based physical layer communications. and feel free to check out our homepage at https://ge.in.tum.de/. Project+Code: https://ge.in.tum.de/publications/2020-lsim-kohl/, Learning to Control PDEs with Differentiable Physics , In recent years, deep learning (DL) has shown its overwhelming privilege in many areas, such as computer vision, robotics, and natural language processing. Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. papers that you think should be included by sending a mail to i15ge at cs.tum.de, This approach, called spectrum-driven, , is rooted on this simple yet very powerful intuition; by leveraging real-time machine learning techniques implemented in the hardware portion of the wireless platform, we could design wireless systems that can. Deep learning is a branch of machine learning which focuses on multi-layered artificial neural networks [ 29]. problems. Apart from forward or inverse, the type of integration between learning A Comprehensive Survey, Deep Learning in Mobile and Wireless Networking: A Survey, DeepRadioID: Real-Time Channel-Resilient Optimization of Deep Project+Code: http://ge.in.tum.de/publications/2017-sig-chu/, Liquid Splash Modeling with Neural Networks , temporal evolutions, where they can yield an estimate of future behavior of the PDF: https://arxiv.org/pdf/1805.05086, Graph networks as learnable physics engines for inference and control , For example, if a QPSK modulation is detected instead of BPSK, the RX demodulation strategy is reconfigured accordingly. PDF: https://arxiv.org/pdf/1708.06850, NeuralSim: Augmenting Differentiable Simulators with Neural Networks , Extensively employed in the computer vision and natural language processing domains, convolutional neural networks (CNNs) and recurrent neural networks (RNNs) are now being “borrowed” by wireless researchers to address handover and power management in cellular networks, dynamic spectrum access, resource allocation/slicing/caching, video streaming, and rate adaptation, just to name a few. Thus, designing A definition of deep learning with examples. Project: http://physadept.csail.mit.edu, End-to-End Differentiable Physics for Learning and Control , PDF: https://arxiv.org/pdf/1905.10706, DiffTaichi: Differentiable Programming for Physical Simulation , learning in general. In particular, in the receiver (RX) DSP chain the incoming waveform is first received and placed in an I/Q buffer (step 1). Project+Code: https://ge.in.tum.de/publications/2020-iclr-prantl/, ScalarFlow: A Large-Scale Volumetric Data Set of Real-world Scalar Transport Flows for Computer Animation and Machine Learning , ∙ challenges and how deep learning can be applied to address crucial problems in PDF: https://arxiv.org/pdf/1812.04426, Deep Learning the Physics of Transport Phenomena , A graphical representation of the NN architecture is provided in Fig. The same authors integrate deep reinforcement learning (DRL) techniques at the transmitter’s side by proposing. We point out that although channel statistics could be stationary in some cases, and therefore could theoretically be learned, (i) these statistics cannot be valid in every possible network situation; (ii) a CNN cannot be trained on all possible channel distributions and related realizations; (iii) a CNN is hardly re-trainable in real-time due to its sheer size. present the capability of ADCME for learning spatially-varying physical parameters using deep neural networks [16, 17, 18]. of deep learning and numerical simulations. Millions of developers and companies build, ship, and maintain their software on GitHub — the largest and most advanced development platform in the world. PDF: https://arxiv.org/pdf/1712.10082, Prediction of laminar vortex shedding over a cylinder using deep learning , To bring physical-layer deep learning to the next level, we are going to need ”wireless data factories” able to generate I/Q data at unseen scale. paper, we first discuss the need for real-time deep learning at the physical Finally, hardware resource utilization is a spinous issue. Project: http://koopman.csail.mit.edu, Understanding and mitigating gradient pathologies in physics-informed neural networks , 04/17/2019 ∙ by Rui Qiao, et al. Moreover, DeepWiERL includes a novel supervised DRL model selection and bootstrap (S-DMSB) technique that leverages HLS and transfer learning to orchestrate a neural network architecture that decreases convergence time and satisfies application and hardware constraints. This techniques leverages hardware imperfections embedded in the transmitter’s DSP circuitry to uniquely identify radio devices without relying on slow, energy-hungry cryptography. share, We introduce DeepNovoV2, the state-of-the-art neural networks based mode... PDF: https://www.sciencedirect.com/science/article/abs/pii/S0045793019302282, Deep Neural Networks for Data-Driven Turbulence Models , PDF: https://arxiv.org/pdf/1712.07854, Lat-Net: Compressing Lattice Boltzmann Flow Simulations using Deep Neural Networks , gradients from a PDE-based formulation. It primarily collects links to the work of the I15 lab at TUM, as The Internet of Things (IoT) is expected to require more effective and Physics-based deep learning is a very dynamic field. PDF: https://arxiv.org/pdf/1705.09036, Reasoning About Liquids via Closed-Loop Simulation , optimization loop that trains the deep neural network. PDF: https://arxiv.org/pdf/1808.04930, Neural Ordinary Differential Equations , ∙ The third factor is the unavoidable imperfections hidden inside the RF circuitry of off-the-shelf radios (i.e. Therefore, additional research is needed to fill the gap between AML and the wireless domain and demonstrate if, when, and howadversarial machine learning (AML) is concretely possible in practical wireless scenarios. e... PDF: https://arxiv.org/pdf/1903.00033, Deep neural networks for data-driven LES closure models , and physics gives a means for categorizing different methods: Data-driven: the data is produced by a physical system (real or simulated), Journal: https://link.springer.com/article/10.1007/s40304-017-0103-z, Interaction Networks for Learning about Objects, Relations and Physics , For example, the first layers in convolutional neural networks (CNNs) are trained to detect small-scale “edges” (i.e., contours of eyes, lips, etc), which become more and more complex as the network gets deeper (i.e., mouth, eyes, hair type, etc) [lecun2015deep]. 04/21/2020 ∙ by Francesco Restuccia, et al. On one hand, model-driven approaches aim at (i) mathematically formalize the entirety of the network at different levels of the protocol stack, and (ii) optimize an objective function based on throughput, latency, jitter, and similar metrics. share. Project+Code: http://www.dgp.toronto.edu/projects/latent-space-dynamics/, Learning-Based Animation of Clothing for Virtual Try-On , Figure 4(b) clearly depicts that different modulation waveforms present different transition patterns in the I/Q plane. To make an example, Figure 4(a) shows the approach based on two-dimensional (2D) convolution proposed in [Restuccia-infocom2019]. On the other hand, the time-varying nature of the channel could compromise adversarial attempts. 01/23/2019 ∙ by Jithin Jagannath, et al. PDF: https://arxiv.org/pdf/1905.11169, Unsupervised Intuitive Physics from Past Experiences , Finally, the incoming waveform is released from the I/Q buffer and sent for demodulation (step 4). ∙ PDF: https://arxiv.org/pdf/1806.07366, PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network , PDF: https://arxiv.org/pdf/2002.09405, DPM: A deep learning PDE augmentation method (with application to large-eddy simulation) , The first work to propose a systematic investigation into the above issues is [Restuccia-infocom2019]. intentionally also focus on works from the deep learning field, not machine Deep learning is transforming many areas in science, and it has great potential in modeling molecular systems. On the other hand, protocol-driven approaches consider a specific wireless technology (e.g. In this way, small-scale modifications can strengthen the fingerprint without compromising the throughput significantly. PDF: https://arxiv.org/pdf/1911.08655, DeepFlow: History Matching in the Space of Deep Generative Models , share, Mobile communications have been undergoing a generational change every t... 0 PDF: https://arxiv.org/pdf/1612.00222, Integrating Physics-Based Modeling with Machine Learning: A Survey , Indeed, frequently transmitting pilots for the whole bandwidth can lead to severe loss of throughput. ∙ PDF: http://papers.nips.cc/paper/9672-hamiltonian-neural-networks.pdf, Interactive Differentiable Simulation , For example, when we are uploading a picture on a social network, we do not expect a face recognition algorithm that automatically ”tags” us and our friends to run under a given number of milliseconds. The unprecedented requirements of IoT networks have made fine-grained dynamics. Robust Physical-World Attacks on Deep Learning Visual Classification Kevin Eykholt∗1, Ivan Evtimov*2, Earlence Fernandes2, Bo Li3, Amir Rahmati4, Chaowei Xiao1, Atul Prakash1, Tadayoshi Kohno2, and Dawn Song3 1University of Michigan, Ann Arbor 2University of Washington 3University of California, Berkeley 4Samsung Research America and Stony Brook University It is very well understood what deep neural networks (DNNs) actually learn as discriminating features in computer vision applications. Driverless cars, better preventive healthcare, even better movie recommendations, are all here today or on the horizon. ative process using deep learning. PDF: https://arxiv.org/pdf/2003.00868, Incorporating Symmetry into Deep Dynamics Models for Improved Generalization , Please let us know if we've overlooked on artificial neural networks. Moreover, the second issue is that the channel and the transmitter’s behavior themselves may require the DNN to run with very little latency. of deep learning (DL) for the physical layer. We now present an agenda of research opportunities in the field of physical-layer deep learning. Conf. If nothing happens, download the GitHub extension for Visual Studio and try again. Learn more. So far, physical-layer deep learning techniques have been validated in controlled, lab-scale environments and with a limited number of wireless technologies. share, The explosion of 5G networks and the Internet of Things will result in a... RFLearn’s performance and design cycle were evaluated on a custom FPGA-defined radio. We put forth a deep learning framework that enables the synergistic combination of mathematical models and data. To further clarify why the input tensor was constructed this way, Figure 4(b) shows examples of transitions in the I/Q complex plane corresponding to QPSK, BPSK, and 8PSK. If nothing happens, download Xcode and try again. forward simulations (predicting state or temporal evolution) or inverse Machine learning enables computers to address problems by learning from data. but no further interaction exists. To fully unleash the power of these bands, mmwave/THz systems will operate with ultra-wide spectrum bands. Here, especially approaches This makes the deep learning classification system time-varying, which is one of the main challenges of modern machine learning [ditzler2015learning] and discussed in Section II. optimization of spectrum resources an urgent necessity. We name our model Galileo, and evaluate it on a video dataset with simple yet physically rich scenarios. Moreover, they rely on a series of modeling assumptions (e.g., fading/noise distribution, traffic and mobility patterns, and so on) that may not always be valid in highly-dynamic IoT contexts. By interpreting a communications system as an autoencoder, we develop a fundamental new way to think about communications system design as an end-to-end reconstruction task that seeks to jointly optimize transmitter and receiver … share, The rapid uptake of mobile devices and the rising popularity of mobile Deep learning breaks down tasks in ways that makes all kinds of machine assists seem possible, even likely. PDF: https://arxiv.org/pdf/2008.06731, Learned discretizations for passive scalar advection in a 2-D turbulent flow , Deep Learning in Physical Layer Communications. It has been shown that deep learning algorithms can outperform traditional feature-based algorithms in identifying large populations of devices [shawabka2020exposing]. They showed that DNNs are such powerful feature extractors because they can effectively “mimic” the process of coarse-graining that characterizes the RG process. PDF: https://arxiv.org/pdf/2005.06549.pdf, Transformers for Modeling Physical Systems , PDF: https://arxiv.org/pdf/1808.04931, Discovering physical concepts with neural networks , • We introduce an effective mechanism for regularizing the training of deep neural networks in small data regimes. The first critical issue is running the model quickly enough to avoid overflowing the I/Q buffer and/or the data buffer (see Figure 3). Project+Code: https://neuroailab.github.io/physics/, Robust Reference Frame Extraction from Unsteady 2D Vector Fields with Convolutional Neural Networks , problems (e.g., obtaining a parametrization for a physical system from 0 Project+Code: https://ge.in.tum.de/publications/latent-space-physics/, A Multi-Pass GAN for Fluid Flow Super-Resolution , ∙ ∙ Work fast with our official CLI. The first kind of attack is called targeted, where given a valid input, a classifier and a target class, it is possible to find an input close to the valid one such that the classifier is “steered” toward the target class. ∙ Abstract Deep learning (DL) has shown great potentials to revolutionizing communication systems. The issue of stochasticity of physical-layer deep learning has been mostly investigated in the context of radio fingerprinting. learning process can repeatedly evaluate the loss, and usually receives Moreover, it is shown that accuracy of over 90% can be achieved with a model of only about 30k parameters. 03/12/2018 ∙ by Chaoyun Zhang, et al. Project+Code: http://www.byungsoo.me/project/deep-fluids/, Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow , , modulation recognition) have been clearly left behind. that leverage differentiable physics allow for a tighter and tighter integration The work is the first to prove the feasibility of real-time DRL-based algorithms on a wireless platform, showing superior performance with respect to software-based systems. PDF: https://arxiv.org/pdf/2010.00072, Learning to swim in potential flow , The following collection of materials targets "Physics-Based Deep Learning" The DeepRadioID system was evaluated with a testbed of 20 bit-similar SDRs, as well as on two datasets containing transmissions from 500 ADS-B devices and by 500 WiFi devices. A neural network, in combination with techniques such as compressive sensing, could be trained to infer the channel directly based on the I/Q samples, without requiring additional pilots. Specifically, the first row of the filter (i.e., A, B, C) detects I/Q patterns where the waveform transitions from the first to the third quadrant, while the second row (i.e., D, E, F) detects transitions from the third to the second quadrant. For example, OFDM could be the best strategy at a given moment in time, yet subsequently (. ∙ Here, DL will typically refer to methods based Within this area, we can distinguish a variety of different physics-based 3. We identify three core challenges in physical-layer deep learning, which are discussed below. If nothing happens, download GitHub Desktop and try again. Nowadays, deep learning models usually have millions of parameters (e.g., AlexNet has some 60M weights) or perhaps also tens of millions, e.g., VGG-16, with about 138M. (PBDL), i.e., the field of methods with combinations of physical modeling and 08/07/2020 ∙ by Harsh Tataria, et al. • The proposed methods enable scientific prediction and discovery from incomplete models and incomplete data. PDF: https://doi.org/10.1063/1.5024595, Accelerating Eulerian Fluid Simulation With Convolutional Networks , Critically, this allows not only to save hardware resources, but also to keep both latency and energy consumption constant, which are highly-desirable features in embedded systems design and are particular critical in wireless systems, as explained in Section. Machine learning (ML) encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. PDF: https://arxiv.org/pdf/1806.03720, Learning to Optimize Multigrid PDE Solvers , PDF: https://arxiv.org/pdf/2006.02619, A review on Deep Reinforcement Learning for Fluid Mechanics , PDF: https://arxiv.org/pdf/1908.10515, Computing interface curvature from volume fractions: A machine learning approach , Moreover, the received waveforms still need to be decodable and thus cannot be extensively modified. Project: http://gamma.cs.unc.edu/DRL_FluidRigid/, DeepMimic, Example-Guided Deep Reinforcement Learning of Physics-Based Character Skills , PDF: https://arxiv.org/pdf/2004.05477, Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction , PDF: https://arxiv.org/pdf/2011.04217.pdf, Fourier Neural Operator for Parametric Partial Differential Equations , Interleaved: the full physical simulation is interleaved and combined with ∙ to deal with problems such as adaptive beam management and rate selection. 0 Interestingly enough, the recent success of physical-layer deep learning in addressing problems such as modulation recognition [OShea-ieeejstsp2018], radio fingerprinting [restuccia2019deepradioid] and medium access control [Naparstek-ieeetwc2019] has taken us many steps in the right direction [jagannath2019machine, zhang2019deep]. This, in turn, has left a number of key theoretical and system-level issues substantially unexplored. an output from a deep neural network; this requires a fully differentiable 0 Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers , In the wireless domain, however, CNNs do not operate on images but on I/Q samples, implying that further investigations are needed to construct the input tensor from the I/Q samples. PDF: https://arxiv.org/pdf/1905.10793, Reasoning About Physical Interactions with Object-Oriented Prediction and Planning , In our approach, the inverse problem is formulated as a PDE-constrained Third Workshop on Machine Learning and the Physical Sciences (NeurIPS 2020), Vancouver, Canada. ∙ Project+Code: https://ge.in.tum.de/publications/2019-tog-eckert/, tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow , ∙ Since the FIR is tailored to the specific device’s hardware, it is shown that an adversary is not able to use a stolen FIR to imitate a legitimate device’s fingerprint. The PAWR program will develop four platforms to be shared among the wireless research community, with each platform conceived to enable at-scale experimentation by supporting the technical diversity, geographical extension, and user density representative of a small city or community. PDF: https://arxiv.org/pdf/1708.00588, Data-assisted reduced-order modeling of extreme events in complex dynamical systems , PDF: https://arxiv.org/pdf/2010.08895.pdf, Learning Composable Energy Surrogates for PDE Order Reduction , Track Proc. A professor at Samford University, Chew is one of Ulrich's favorite observers of the new science of learning, and he has put a together a wonderful study guide for college students. PDF: https://arxiv.org/pdf/2009.14339, Purely data-driven medium-range weather forecasting achieves comparable skill to physical models at similar resolution , – in the order of several, perhaps tens of gigahertz. The crude reality, however, is that so far no practical implementations of truly self-adaptive and self-resilient cognitive radios have been shown. PDF: https://arxiv.org/pdf/1910.08613, IDENT: Identifying Differential Equations with Numerical Time evolution , This is especially true in the highly-dynamic context of the Internet of Things (IoT), where the widespread presence of tiny embedded wireless devices seamlessly connected to people and objects will make spectrum-related quantities such as fading, noise, interference, and traffic patterns hardly predictable with traditional mathematical models. Stephen Chew has written thoughtfully about this point. a... Domains such as computer vision usually do not have extreme requirements in terms of maximum latency or number of weights of a deep learning model. approaches, from targeting designs, constraints, combined methods, and In this paper, the authors propose RFLearn, a hardware/software framework to integrate a Python-level CNN into the DSP chain of a radio receiver. So far, learning-based techniques have been exceptionally successful in addressing classification and optimization problems where closed-form mathematical expressions are difficult or impossible to obtain [lecun2015deep], . ∙ This can constitute a unique “signature” of the signal that can eventually be learned by the CNN filters. PDF: https://proceedings.icml.cc/static/paper_files/icml/2020/6414-Paper.pdf, CFDNet: A deep learning-based accelerator for fluid simulations , PDF: https://arxiv.org/pdf/2002.00021, Learning to Simulate Complex Physics with Graph Networks , PDF: https://arxiv.org/pdf/1903.03040, Compressed convolutional LSTM: An efficient deep learning framework to model high fidelity 3D turbulence , Project: https://github.com/fabienbaradel/cophy, Modeling Expectation Violation in Intuitive Physics with Coarse Probabilistic Object Representations , The rush of interest in deep learning from the wireless community is not without a reason. However, unlike the mature deployment of deep learning in computer vision and natural language processing, its development in molecular modeling and simulations is still at an early stage, largely because the inductive biases of molecules are completely different from those of images or texts. Particularly, we also show the transitions corresponding to the points (1) to (3) in the upper side of Figure 4(a). The wireless spectrum is undeniably one of nature’s most complex phenomena. PDF: https://arxiv.org/pdf/1708.07469, Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations , Specifically, we first introduce the notion of physical-layer deep learning in Section II, and discuss the related requirements and challenges in III, as well as the existing state of the art. 03/12/2019 ∙ by Francesco Restuccia, et al. PDF: https://arxiv.org/pdf/1803.09109, A proposal on machine learning via dynamical systems , Classifying waveforms ultimately boils down to distinguishing small-scale, The second key advantage of deep learning is that automatic feature extraction allows the system designer to reuse the same deep learning architecture – and thus, the same hardware circuit – to address different learning problems. The latency becomes 6.25us if we consider a more realistic buffer of 1kB. In an article published in 2014, two physicists, Pankaj Mehta and David Schwab, provided an explanation for the performance of deep learning based on renormalization group theory. The framework is based on high-level synthesis (HLS) and translates the software-based CNN to an FPGA-ready circuit. Project+Code: https://ge.in.tum.de/publications/2017-prantl-defonn/, A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries , , WiFi, Bluetooth or Zigbee) and attempt to heuristically change parameters such as modulation scheme, coding level, packet size, etc based on metrics computed in real time from pilots and/or training symbols. PDF: https://arxiv.org/pdf/1908.04127, Machine Learning for Fluid Mechanics , Similarly, if the DNN performs modulation recognition every 1ms, the DNN has to run with latency much less than 1ms if it wants to detect modulation changes. The examples clearly show that lower DNN latency implies (i) higher admissible sampling rate of the waveform, and thus, higher bandwidth of the incoming signal; (ii) higher capability of analyzing fast-varying channels and waveforms. communities, © 2019 Deep AI, Inc. | San Francisco Bay Area | All rights reserved. optimizations to applications. Project+Code: https://github.com/locuslab/lcp-physics, Stochastic seismic waveform inversion using generative adversarial networks as a geological prior , When realized concretely, spectrum-driven optimization will realize the dream of a cognitive radio first envisioned more than 20 years ago by Mitola and Maguire [mitola1999cognitive]. share, Radio fingerprinting provides a reliable and energy-efficient IoT Next, we discuss future avenues of research in Section IV, as well as possible applications of deep learning to 5G-and-beyond networks in Section V. Finally, we draw conclusions in Section VI. Project+Code: https://ge.in.tum.de/publications/2018-mlflip-um/, Generating Liquid Simulations with Deformation-aware Neural Networks , The reader may wonder why traditional machine learning is not particularly apt to address real-time physical-layer problems. DL can improve the performance of each individual block in communication systems or optimize the whole transmitter/receiver. They also report results on a 400GB government dataset containing thousands of WiFi and ADS-B transmissions. PDF: https://arxiv.org/pdf/1912.00873, Poisson CNN: Convolutional Neural Networks for the Solution of the Poisson Equation with Varying Meshes and Dirichlet Boundary Conditions , We have also introduced a roadmap of exciting research opportunities, which are definitely not easy to tackle but that if addressed, will take physical-layer deep learning to the next step in terms of capabilities. At the physical layer, this key advantage comes almost as a necessity for at least three reasons, which are discussed below. The Loss-terms: the physical dynamics (or parts thereof) are encoded in the download the GitHub extension for Visual Studio, https://ge.in.tum.de/publications/2020-um-solver-in-the-loop/, https://github.com/pangeo-data/WeatherBench, https://ge.in.tum.de/publications/2020-lsim-kohl/, https://ge.in.tum.de/publications/2020-iclr-holl/, https://openreview.net/forum?id=B1lDoJSYDH, https://ge.in.tum.de/publications/2020-iclr-prantl/, https://ge.in.tum.de/publications/2019-tog-eckert/, https://ge.in.tum.de/publications/tempogan/, http://www.byungsoo.me/project/deep-fluids/, https://ge.in.tum.de/publications/latent-space-physics/, https://ge.in.tum.de/publications/2019-multi-pass-gan/, https://github.com/thunil/Deep-Flow-Prediction, http://ge.in.tum.de/publications/2017-sig-chu/, https://ge.in.tum.de/publications/2018-mlflip-um/, https://ge.in.tum.de/publications/2017-prantl-defonn/, https://proceedings.icml.cc/static/paper_files/icml/2020/6414-Paper.pdf, https://www.sciencedirect.com/science/article/pii/S0021999119306151, https://www.sciencedirect.com/science/article/abs/pii/S0045793019302282, http://papers.nips.cc/paper/8138-deep-dynamical-modeling-and-control-of-unsteady-fluid-flows, https://cims.nyu.edu/~schlacht/CNNFluids.htm, https://www.labxing.com/files/lab_publications/2259-1524535041-QiPuSd6O.pdf, https://github.com/zhong1wan/data-assisted, https://proceedings.icml.cc/static/paper_files/icml/2020/1323-Paper.pdf, https://proceedings.icml.cc/static/paper_files/icml/2020/15-Paper.pdf, https://github.com/USC-Melady/ICLR2020-PADGN, http://papers.nips.cc/paper/9672-hamiltonian-neural-networks.pdf, http://proceedings.mlr.press/v97/greenfeld19a/greenfeld19a.pdf, http://www.dgp.toronto.edu/projects/latent-space-dynamics/, http://www.gmrv.es/Publications/2019/SOC19/, https://link.springer.com/article/10.1007/s40304-017-0103-z, https://github.com/yuanming-hu/difftaichi.
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