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Jared Willard

Other affiliations: United States Geological Survey
Bio: Jared Willard is an academic researcher from University of Minnesota. The author has contributed to research in topics: Computer science & Mean squared error. The author has an hindex of 6, co-authored 14 publications receiving 375 citations. Previous affiliations of Jared Willard include United States Geological Survey.

Papers
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Posted Content
01 Jan 2020
TL;DR: An overview of techniques to integrate machine learning with physics-based modeling and classes of methodologies used to construct physics-guided machine learning models and hybrid physics-machine learning frameworks from a machine learning standpoint is provided.
Abstract: In this manuscript, we provide a structured and comprehensive overview of techniques to integrate machine learning with physics-based modeling. First, we provide a summary of application areas for which these approaches have been applied. Then, we describe classes of methodologies used to construct physics-guided machine learning models and hybrid physics-machine learning frameworks from a machine learning standpoint. With this foundation, we then provide a systematic organization of these existing techniques and discuss ideas for future research.

230 citations

Book ChapterDOI
31 Jan 2019
TL;DR: It is shown that a PGRNN can improve prediction accuracy over that of physical models, while generating outputs consistent with physical laws, and achieving good generalizability.
Abstract: This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physical models, while generating outputs consistent with physical laws, and achieving good generalizability. Standard RNNs, even when producing superior prediction accuracy, often produce physically inconsistent results and lack generalizability. We further enhance this approach by using a pre-training method that leverages the simulated data from a physics-based model to address the scarcity of observed data. The PGRNN has the flexibility to incorporate additional physical constraints and we incorporate a density-depth relationship. Both enhancements further improve PGRNN performance. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where mechanistic (also known as process-based) models are used, e.g., power engineering, climate science, materials science, computational chemistry, and biomedicine.

190 citations

Journal ArticleDOI
TL;DR: In this paper, the authors presented the results of the North Central Climate Adaptation Science Center (NCAACS) at the University of Minnesota (U.M. System) with the help of the National Science Foundation (NSF).
Abstract: Department of the Interior Northeast Climate Adaptation Science Center; Midwest Glacial Lakes Fish Habitat Partnership grant through FWS; NSF Expedition in Computing Grant [1029711]; NSFNational Science Foundation (NSF) [EAR-PF-1725386]; Digital Technology Center at the University of MinnesotaUniversity of Minnesota System; Department of the Interior North Central Climate Adaptation Science Center; North Temperate Lakes Long-Term Ecological Research [NSF DEB-1440297]; Global Lake Ecological Observatory Network [NSF 1702991]

188 citations

Posted Content
TL;DR: This article proposed a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improves the modeling of physical processes.
Abstract: Physics-based models of dynamical systems are often used to study engineering and environmental systems. Despite their extensive use, these models have several well-known limitations due to simplified representations of the physical processes being modeled or challenges in selecting appropriate parameters. While-state-of-the-art machine learning models can sometimes outperform physics-based models given ample amount of training data, they can produce results that are physically inconsistent. This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improves the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physics-based models, while generating outputs consistent with physical laws. An important aspect of our PGRNN approach lies in its ability to incorporate the knowledge encoded in physics-based models. This allows training the PGRNN model using very few true observed data while also ensuring high prediction accuracy. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where physics-based (also known as mechanistic) models are used, e.g., climate science, materials science, computational chemistry, and biomedicine.

88 citations

Journal ArticleDOI
17 May 2021
TL;DR: It is shown that a PGRNN can improve prediction accuracy over that of physics-based models, while generating outputs consistent with physical laws, and is applicable more widely to a range of scientific and engineering disciplines where physics- based models are used.
Abstract: Physics-based models are often used to study engineering and environmental systems. The ability to model these systems is the key to achieving our future environmental sustainability and improving the quality of human life. This article focuses on simulating lake water temperature, which is critical for understanding the impact of changing climate on aquatic ecosystems and assisting in aquatic resource management decisions. General Lake Model (GLM) is a state-of-the-art physics-based model used for addressing such problems. However, like other physics-based models used for studying scientific and engineering systems, it has several well-known limitations due to simplified representations of the physical processes being modeled or challenges in selecting appropriate parameters. While state-of-the-art machine learning models can sometimes outperform physics-based models given ample amount of training data, they can produce results that are physically inconsistent. This article proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improves the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physics-based models (by over 20% even with very little training data), while generating outputs consistent with physical laws. An important aspect of our PGRNN approach lies in its ability to incorporate the knowledge encoded in physics-based models. This allows training the PGRNN model using very few true observed data while also ensuring high prediction accuracy. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where physics-based (also known as mechanistic) models are used.

81 citations


Cited by
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Journal ArticleDOI
TL;DR: It is shown that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent, which made it possible to formulate a variational principle for the force-free magnetic fields.
Abstract: where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

1,858 citations

Journal ArticleDOI
TL;DR: This work reviews the recent status of methodologies and techniques related to the construction of digital twins mostly from a modeling perspective to provide a detailed coverage of the current challenges and enabling technologies along with recommendations and reflections for various stakeholders.
Abstract: Digital twin can be defined as a virtual representation of a physical asset enabled through data and simulators for real-time prediction, optimization, monitoring, controlling, and improved decision making. Recent advances in computational pipelines, multiphysics solvers, artificial intelligence, big data cybernetics, data processing and management tools bring the promise of digital twins and their impact on society closer to reality. Digital twinning is now an important and emerging trend in many applications. Also referred to as a computational megamodel, device shadow, mirrored system, avatar or a synchronized virtual prototype, there can be no doubt that a digital twin plays a transformative role not only in how we design and operate cyber-physical intelligent systems, but also in how we advance the modularity of multi-disciplinary systems to tackle fundamental barriers not addressed by the current, evolutionary modeling practices. In this work, we review the recent status of methodologies and techniques related to the construction of digital twins mostly from a modeling perspective. Our aim is to provide a detailed coverage of the current challenges and enabling technologies along with recommendations and reflections for various stakeholders.

660 citations

Posted Content
TL;DR: From smart grids to disaster management, high impact problems where existing gaps can be filled by ML are identified, in collaboration with other fields, to join the global effort against climate change.
Abstract: Climate change is one of the greatest challenges facing humanity, and we, as machine learning experts, may wonder how we can help. Here we describe how machine learning can be a powerful tool in reducing greenhouse gas emissions and helping society adapt to a changing climate. From smart grids to disaster management, we identify high impact problems where existing gaps can be filled by machine learning, in collaboration with other fields. Our recommendations encompass exciting research questions as well as promising business opportunities. We call on the machine learning community to join the global effort against climate change.

441 citations

Journal ArticleDOI
14 Jul 2020
TL;DR: A review of physical lake variables and their responses to climate change is presented in this paper, where the authors discuss recent and expected lake responses and look towards future research opportunities in lake monitoring and modelling.
Abstract: Climate change is one of the most severe threats to global lake ecosystems. Lake surface conditions, such as ice cover, surface temperature, evaporation and water level, respond dramatically to this threat, as observed in recent decades. In this Review, we discuss physical lake variables and their responses to climate change. Decreases in winter ice cover and increases in lake surface temperature modify lake mixing regimes and accelerate lake evaporation. Where not balanced by increased mean precipitation or inflow, higher evaporation rates will favour a decrease in lake level and surface water extent. Together with increases in extreme-precipitation events, these lake responses will impact lake ecosystems, changing water quantity and quality, food provisioning, recreational opportunities and transportation. Future research opportunities, including enhanced observation of lake variables from space (particularly for small water bodies), improved in situ lake monitoring and the development of advanced modelling techniques to predict lake processes, will improve our global understanding of lake responses to a changing climate. Climate change affects lakes worldwide and is predicted to continue to alter lake ice cover, surface temperature, evaporation rates, water levels and mixing regimes. This Review discusses recent and expected lake responses to climate change and looks towards future research opportunities in lake monitoring and modelling.

412 citations

Journal Article
TL;DR: This work introduces a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data.
Abstract: We introduce a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is first-principles based in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DPMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size.

254 citations