arXiv subjects

Anuj Karpatne

Publications and source records attributed to Anuj Karpatne.

50 records · Page 3Linked to original sources

arXiv2021

Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs

We propose quadratic residual networks (QRes) as a new type of parameter-efficient neural network architecture, by adding a quadratic residual term to the weighted sum of inputs before applying activation functions. With sufficiently high functional capacity (or expressive power), we show that it is especially powerful for solving forward and inverse physics problems involving partial differential equations (PDEs). Using tools from algebraic geometry, we theoretically demonstrate that, in contrast to plain neural networks, QRes shows better parameter efficiency in terms of network width and depth thanks to higher non-linearity in every neuron. Finally, we empirically show that QRes shows faster convergence speed in terms of number of training epochs especially in learning complex patterns.

cs.LG↗

arXiv2021

Maximizing Cohesion and Separation in Graph Representation Learning: A Distance-aware Negative Sampling Approach

The objective of unsupervised graph representation learning (GRL) is to learn a low-dimensional space of node embeddings that reflect the structure of a given unlabeled graph. Existing algorithms for this task rely on negative sampling objectives that maximize the similarity in node embeddings at nearby nodes (referred to as "cohesion") by maintaining positive and negative corpus of node pairs. While positive samples are drawn from node pairs that co-occur in short random walks, conventional approaches construct negative corpus by uniformly sampling random pairs, thus ignoring valuable information about structural dissimilarity among distant node pairs (referred to as "separation"). In this paper, we present a novel Distance-aware Negative Sampling (DNS) which maximizes the separation of distant node-pairs while maximizing cohesion at nearby node-pairs by setting the negative sampling probability proportional to the pair-wise shortest distances. Our approach can be used in conjunction with any GRL algorithm and we demonstrate the efficacy of our approach over baseline negative sampling methods over downstream node classification tasks on a number of benchmark datasets and GRL algorithms. All our codes and datasets are available at https://github.com/Distance-awareNS/DNS/.

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arXiv2020

Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles

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.

cs.LG↗

arXiv2019

Physics-Guided Architecture (PGA) of Neural Networks for Quantifying Uncertainty in Lake Temperature Modeling

To simultaneously address the rising need of expressing uncertainties in deep learning models along with producing model outputs which are consistent with the known scientific knowledge, we propose a novel physics-guided architecture (PGA) of neural networks in the context of lake temperature modeling where the physical constraints are hard coded in the neural network architecture. This allows us to integrate such models with state of the art uncertainty estimation approaches such as Monte Carlo (MC) Dropout without sacrificing the physical consistency of our results. We demonstrate the effectiveness of our approach in ensuring better generalizability as well as physical consistency in MC estimates over data collected from Lake Mendota in Wisconsin and Falling Creek Reservoir in Virginia, even with limited training data. We further show that our MC estimates correctly match the distribution of ground-truth observations, thus making the PGA paradigm amenable to physically grounded uncertainty quantification.

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arXiv2019

Physics-guided Design and Learning of Neural Networks for Predicting Drag Force on Particle Suspensions in Moving Fluids

Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the inability to accurately model a physical process owing to incomplete knowledge about certain facets of the process or due to the underlying process being too complex to accurately encode into a simulation model. In such situations, it is often useful to rely on machine learning methods to fill in the gap by learning a model of the complex physical process directly from simulation data. However, as data generation through simulations is costly, we need to develop models, being cognizant of data paucity issues. In such scenarios it is often helpful if the rich physical knowledge of the application domain is incorporated in the architectural design of machine learning models. Further, we can also use information from physics-based simulations to guide the learning process using aggregate supervision to favorably constrain the learning process. In this paper, we propose PhyDNN, a deep learning model using physics-guided structural priors and physics-guided aggregate supervision for modeling the drag forces acting on each particle in a Computational Fluid Dynamics-Discrete Element Method(CFD-DEM). We conduct extensive experiments in the context of drag force prediction and showcase the usefulness of including physics knowledge in our deep learning formulation both in the design and through learning process. Our proposed PhyDNN model has been compared to several state-of-the-art models and achieves a significant performance improvement of 8.46% on average across all baseline models. The source code has been made available and the dataset used is detailed in [1, 2].

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arXiv2019

A Fast-Optimal Guaranteed Algorithm For Learning Sub-Interval Relationships in Time Series

Traditional approaches focus on finding relationships between two entire time series, however, many interesting relationships exist in small sub-intervals of time and remain feeble during other sub-intervals. We define the notion of a sub-interval relationship (SIR) to capture such interactions that are prominent only in certain sub-intervals of time. To that end, we propose a fast-optimal guaranteed algorithm to find most interesting SIR relationship in a pair of time series. Lastly, we demonstrate the utility of our method in climate science domain based on a real-world dataset along with its scalability scope and obtain useful domain insights.

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arXiv2019

Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profiles

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.

physics.comp-ph↗

arXiv2018

Physics Guided Recurrent Neural Networks For Modeling Dynamical Systems: Application to Monitoring Water Temperature And Quality In Lakes

In this paper, we introduce a novel framework for combining scientific knowledge within physics-based models and recurrent neural networks to advance scientific discovery in many dynamical systems. We will first describe the use of outputs from physics-based models in learning a hybrid-physics-data model. Then, we further incorporate physical knowledge in real-world dynamical systems as additional constraints for training recurrent neural networks. We will apply this approach on modeling lake temperature and quality where we take into account the physical constraints along both the depth dimension and time dimension. By using scientific knowledge to guide the construction and learning the data-driven model, we demonstrate that this method can achieve better prediction accuracy as well as scientific consistency of results.

cs.LG↗

arXiv2018

Mining Sub-Interval Relationships In Time Series Data

Time-series data is being increasingly collected and stud- ied in several areas such as neuroscience, climate science, transportation, and social media. Discovery of complex patterns of relationships between individual time-series, using data-driven approaches can improve our understanding of real-world systems. While traditional approaches typically study relationships between two entire time series, many interesting relationships in real-world applications exist in small sub-intervals of time while remaining absent or feeble during other sub-intervals. In this paper, we define the notion of a sub-interval relationship (SIR) to capture inter- actions between two time series that are prominent only in certain sub-intervals of time. We propose a novel and efficient approach to find most interesting SIR in a pair of time series. We evaluate our proposed approach on two real-world datasets from climate science and neuroscience domain and demonstrated the scalability and computational efficiency of our proposed approach. We further evaluated our discovered SIRs based on a randomization based procedure. Our results indicated the existence of several such relationships that are statistically significant, some of which were also found to have physical interpretation.

stat.ML↗

arXiv2017

Discovery of Shifting Patterns in Sequence Classification

In this paper, we investigate the multi-variate sequence classification problem from a multi-instance learning perspective. Real-world sequential data commonly show discriminative patterns only at specific time periods. For instance, we can identify a cropland during its growing season, but it looks similar to a barren land after harvest or before planting. Besides, even within the same class, the discriminative patterns can appear in different periods of sequential data. Due to such property, these discriminative patterns are also referred to as shifting patterns. The shifting patterns in sequential data severely degrade the performance of traditional classification methods without sufficient training data. We propose a novel sequence classification method by automatically mining shifting patterns from multi-variate sequence. The method employs a multi-instance learning approach to detect shifting patterns while also modeling temporal relationships within each multi-instance bag by an LSTM model to further improve the classification performance. We extensively evaluate our method on two real-world applications - cropland mapping and affective state recognition. The experiments demonstrate the superiority of our proposed method in sequence classification performance and in detecting discriminative shifting patterns.

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arXiv2017

Spatio-Temporal Data Mining: A Survey of Problems and Methods

Large volumes of spatio-temporal data are increasingly collected and studied in diverse domains including, climate science, social sciences, neuroscience, epidemiology, transportation, mobile health, and Earth sciences. Spatio-temporal data differs from relational data for which computational approaches are developed in the data mining community for multiple decades, in that both spatial and temporal attributes are available in addition to the actual measurements/attributes. The presence of these attributes introduces additional challenges that needs to be dealt with. Approaches for mining spatio-temporal data have been studied for over a decade in the data mining community. In this article we present a broad survey of this relatively young field of spatio-temporal data mining. We discuss different types of spatio-temporal data and the relevant data mining questions that arise in the context of analyzing each of these datasets. Based on the nature of the data mining problem studied, we classify literature on spatio-temporal data mining into six major categories: clustering, predictive learning, change detection, frequent pattern mining, anomaly detection, and relationship mining. We discuss the various forms of spatio-temporal data mining problems in each of these categories.

cs.LG↗

arXiv2017

ORBIT: Ordering Based Information Transfer Across Space and Time for Global Surface Water Monitoring

Many earth science applications require data at both high spatial and temporal resolution for effective monitoring of various ecosystem resources. Due to practical limitations in sensor design, there is often a trade-off in different resolutions of spatio-temporal datasets and hence a single sensor alone cannot provide the required information. Various data fusion methods have been proposed in the literature that mainly rely on individual timesteps when both datasets are available to learn a mapping between features values at different resolutions using local relationships between pixels. Earth observation data is often plagued with spatially and temporally correlated noise, outliers and missing data due to atmospheric disturbances which pose a challenge in learning the mapping from a local neighborhood at individual timesteps. In this paper, we aim to exploit time-independent global relationships between pixels for robust transfer of information across different scales. Specifically, we propose a new framework, ORBIT (Ordering Based Information Transfer) that uses relative ordering constraint among pixels to transfer information across both time and scales. The effectiveness of the framework is demonstrated for global surface water monitoring using both synthetic and real-world datasets.

cs.LG↗

arXiv2017

Machine Learning for the Geosciences: Challenges and Opportunities

Geosciences is a field of great societal relevance that requires solutions to several urgent problems facing our humanity and the planet. As geosciences enters the era of big data, machine learning (ML) -- that has been widely successful in commercial domains -- offers immense potential to contribute to problems in geosciences. However, problems in geosciences have several unique challenges that are seldom found in traditional applications, requiring novel problem formulations and methodologies in machine learning. This article introduces researchers in the machine learning (ML) community to these challenges offered by geoscience problems and the opportunities that exist for advancing both machine learning and geosciences. We first highlight typical sources of geoscience data and describe their properties that make it challenging to use traditional machine learning techniques. We then describe some of the common categories of geoscience problems where machine learning can play a role, and discuss some of the existing efforts and promising directions for methodological development in machine learning. We conclude by discussing some of the emerging research themes in machine learning that are applicable across all problems in the geosciences, and the importance of a deep collaboration between machine learning and geosciences for synergistic advancements in both disciplines.

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arXiv2017

Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data

Data science models, although successful in a number of commercial domains, have had limited applicability in scientific problems involving complex physical phenomena. Theory-guided data science (TGDS) is an emerging paradigm that aims to leverage the wealth of scientific knowledge for improving the effectiveness of data science models in enabling scientific discovery. The overarching vision of TGDS is to introduce scientific consistency as an essential component for learning generalizable models. Further, by producing scientifically interpretable models, TGDS aims to advance our scientific understanding by discovering novel domain insights. Indeed, the paradigm of TGDS has started to gain prominence in a number of scientific disciplines such as turbulence modeling, material discovery, quantum chemistry, bio-medical science, bio-marker discovery, climate science, and hydrology. In this paper, we formally conceptualize the paradigm of TGDS and present a taxonomy of research themes in TGDS. We describe several approaches for integrating domain knowledge in different research themes using illustrative examples from different disciplines. We also highlight some of the promising avenues of novel research for realizing the full potential of theory-guided data science.

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