DeepMoD: Deep learning for model discovery in noisy data

Both, Gert-Jan; Choudhury, Subham; Sens, Pierre; Kusters, Remy

doi:10.1016/j.jcp.2020.109985

Cited by 82 publications

(74 citation statements)

References 14 publications

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“…( 3) is highly intractable since the ℓ 0 regularization makes this problem np-hard. Though relaxation of the ℓ 0 term by the less rigorous ℓ 1 regularization improves the well-posedness and enables the optimization in a continuous space, false-positive identification occurs where accurate sparsity of the PDE coefficients cannot be realized 44,45 . To address this challenge, we present an alternating direction optimization (ADO) algorithm that divides the overall optimization problem into a set of tractable subproblems to sequentially optimize θ and Λ within a few alternating iterations (denoted by k), namely,…”

Section: Alternating Direction Optimizationmentioning

confidence: 99%

“…Nevertheless, the resulting model is still a "black box" and lacks sufficient interpretability since the closed-form governing equations cannot be uncovered. Latest studies 44,45 show the potential of using DNNs and automatic differentiation to obtain closed-form PDEs, from noisy data, in a constrained search space with a predefined library of PDE terms; yet, false-positive identification occurs due to the use of less rigorous sparse regression along with DNN training. In fact, simultaneously optimizing the DNN parameters and sparse PDE coefficients, while accurately enforcing sparsity, is non-trivial and remains a significant challenge in closed-form PDE discovery.…”

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confidence: 99%

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Physics-informed learning of governing equations from scarce data

2021

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Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel approach called physics-informed neural network with sparse regression to discover governing partial differential equations from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this discovery approach seamlessly integrates the strengths of deep neural networks for rich representation learning, physics embedding, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the equations. The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of partial differential equation systems with different levels of data scarcity and noise accounting for different initial/boundary conditions. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.

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Section: Alternating Direction Optimizationmentioning

confidence: 99%

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confidence: 99%

Physics-informed learning of governing equations from scarce data

2021

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“…Besides, Krishnapriyan et al [27] proposed the characterizing possible failure modes in PINNs from the opposite perspective. More recently, Both et al [28] introduced the DeepMoD for model discovery in noisy data. Also, Lu et al [29] developed a DL library to solve differential equations and dynamic systems.…”

Section: St (2) With Fixed Initial Densitiesmentioning

confidence: 99%

Learning Spacial Domain Infectious Disease Control Model for Vaccine Distribution by Physics-Constraint Machine Learning

Yang

Jiang

et al. 2022

Preprint

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The coronavirus disease, COVID-19, has become a global challenging pandemic. Causing significant loss of life, property, and economics worldwide. The study of infectious disease models allows us to have a deeper understand of spreading trend of highly infectious diseases. Therefore, studying infectious disease models is imminent. In this work, we propose learning spacial domain infectious disease control model for vaccine distribution by physics-constraint machine learning. Usually, these dynamical systems are utilized in epidemiology models to predict the time evolution and development trend of highly infectious diseases such as COVID-19. We reformulate the SIR models and give corresponding policies via dynamical systems. More importantly, we obtain the approximating numerical solution of the systems of dynamical PDEs via the PINNs algorithm, within the acceptable range of approximation error. Additionally, we present several numerical solutions of the PDEs under a variety of scenarios.

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“…Rather than just predicting or making decisions, AI solutions should be developed to conduct exploratory analyses, i.e., to find new, interesting patterns in complex systems or facilitate scientific discovery ( Raghu and Schmidt, 2020 ). Specific cases where this direction has already been explored include e.g., drug discovery ( Vamathevan et al, 2019 ), the discovery of new material ( Butler et al, 2018 ), symbolic math ( Lample and Charton, 2019 ; Stanley et al, 2019 ) or the discovery of new physical laws ( Both et al, 2019 ; Iten et al, 2020 ; Udrescu and Tegmark, 2020 ). Will AI succeed in assisting humans in the discovery of new scientific knowledge?…”

Section: Part I: Artificial Intelligence and Interdisciplinary Researmentioning

confidence: 99%

Interdisciplinary Research in Artificial Intelligence: Challenges and Opportunities

et al. 2020

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The use of artificial intelligence (AI) in a variety of research fields is speeding up multiple digital revolutions, from shifting paradigms in healthcare, precision medicine and wearable sensing, to public services and education offered to the masses around the world, to future cities made optimally efficient by autonomous driving. When a revolution happens, the consequences are not obvious straight away, and to date, there is no uniformly adapted framework to guide AI research to ensure a sustainable societal transition. To answer this need, here we analyze three key challenges to interdisciplinary AI research, and deliver three broad conclusions: 1) future development of AI should not only impact other scientific domains but should also take inspiration and benefit from other fields of science, 2) AI research must be accompanied by decision explainability, dataset bias transparency as well as development of evaluation methodologies and creation of regulatory agencies to ensure responsibility, and 3) AI education should receive more attention, efforts and innovation from the educational and scientific communities. Our analysis is of interest not only to AI practitioners but also to other researchers and the general public as it offers ways to guide the emerging collaborations and interactions toward the most fruitful outcomes.

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DeepMoD: Deep learning for model discovery in noisy data

Cited by 82 publications

References 14 publications

Physics-informed learning of governing equations from scarce data

Physics-informed learning of governing equations from scarce data

Learning Spacial Domain Infectious Disease Control Model for Vaccine Distribution by Physics-Constraint Machine Learning

Interdisciplinary Research in Artificial Intelligence: Challenges and Opportunities

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