Karthik Kashinath

Bio: Karthik Kashinath is an academic researcher from Lawrence Berkeley National Laboratory. The author has contributed to research in topics: Computer science & Physics. The author has an hindex of 18, co-authored 60 publications receiving 1148 citations. Previous affiliations of Karthik Kashinath include University of Cambridge.

Atmospheric River Tracking Method Intercomparison Project(ARTMIP): Project Goals and Experimental Design

Abstract: . The Atmospheric River Tracking Method Intercomparison Project (ARTMIP) is an international collaborative effort to understand and quantify the uncertainties in atmospheric river (AR) science based on detection algorithm alone. Currently, there are many AR identification and tracking algorithms in the literature with a wide range of techniques and conclusions. ARTMIP strives to provide the community with information on different methodologies and provide guidance on the most appropriate algorithm for a given science question or region of interest. All ARTMIP participants will implement their detection algorithms on a specified common dataset for a defined period of time. The project is divided into two phases: Tier 1 will utilize the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2) reanalysis from January 1980 to June 2017 and will be used as a baseline for all subsequent comparisons. Participation in Tier 1 is required. Tier 2 will be optional and include sensitivity studies designed around specific science questions, such as reanalysis uncertainty and climate change. High-resolution reanalysis and/or model output will be used wherever possible. Proposed metrics include AR frequency, duration, intensity, and precipitation attributable to ARs. Here, we present the ARTMIP experimental design, timeline, project requirements, and a brief description of the variety of methodologies in the current literature. We also present results from our 1-month “proof-of-concept” trial run designed to illustrate the utility and feasibility of the ARTMIP project.

Towards Physics-informed Deep Learning for Turbulent Flow Prediction

Abstract: While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim to predict turbulent flow by learning its highly nonlinear dynamics from spatiotemporal velocity fields of large-scale fluid flow simulations of relevance to turbulence modeling and climate modeling. We adopt a hybrid approach by marrying two well-established turbulent flow simulation techniques with deep learning. Specifically, we introduce trainable spectral filters in a coupled model of Reynolds-averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES), followed by a specialized U-net for prediction. Our approach, which we call Turbulent-Flow Net, is grounded in a principled physics model, yet offers the flexibility of learned representations. We compare our model with state-of-the-art baselines and observe significant reductions in error for predictions 60 frames ahead. Most importantly, our method predicts physical fields that obey desirable physical characteristics, such as conservation of mass, whilst faithfully emulating the turbulent kinetic energy field and spectrum, which are critical for accurate prediction of turbulent flows.

Spherical CNNs on Unstructured Grids

Abstract: We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. To this end, we replace conventional convolution kernels with linear combinations of differential operators that are weighted by learnable parameters. Differential operators can be efficiently estimated on unstructured grids using one-ring neighbors, and learnable parameters can be optimized through standard back-propagation. As a result, we obtain extremely efficient neural networks that match or outperform state-of-the-art network architectures in terms of performance but with a significantly lower number of network parameters. We evaluate our algorithm in an extensive series of experiments on a variety of computer vision and climate science tasks, including shape classification, climate pattern segmentation, and omnidirectional image semantic segmentation. Overall, we present (1) a novel CNN approach on unstructured grids using parameterized differential operators for spherical signals, and (2) we show that our unique kernel parameterization allows our model to achieve the same or higher accuracy with significantly fewer network parameters.

The Atmospheric River Tracking Method Intercomparison Project (ARTMIP): Quantifying Uncertainties in Atmospheric River Climatology

Abstract: Author(s): Rutz, JJ; Shields, CA; Lora, JM; Payne, AE; Guan, B; Ullrich, P; O’Brien, T; Leung, LR; Ralph, FM; Wehner, M; Brands, S; Collow, A; Goldenson, N; Gorodetskaya, I; Griffith, H; Kashinath, K; Kawzenuk, B; Krishnan, H; Kurlin, V; Lavers, D; Magnusdottir, G; Mahoney, K; McClenny, E; Muszynski, G; Nguyen, PD; Prabhat, M; Qian, Y; Ramos, AM; Sarangi, C; Sellars, S; Shulgina, T; Tome, R; Waliser, D; Walton, D; Wick, G; Wilson, AM; Viale, M | Abstract: Atmospheric rivers (ARs) are now widely known for their association with high-impact weather events and long-term water supply in many regions. Researchers within the scientific community have developed numerous methods to identify and track of ARs—a necessary step for analyses on gridded data sets, and objective attribution of impacts to ARs. These different methods have been developed to answer specific research questions and hence use different criteria (e.g., geometry, threshold values of key variables, and time dependence). Furthermore, these methods are often employed using different reanalysis data sets, time periods, and regions of interest. The goal of the Atmospheric River Tracking Method Intercomparison Project (ARTMIP) is to understand and quantify uncertainties in AR science that arise due to differences in these methods. This paper presents results for key AR-related metrics based on 20+ different AR identification and tracking methods applied to Modern-Era Retrospective Analysis for Research and Applications Version 2 reanalysis data from January 1980 through June 2017. We show that AR frequency, duration, and seasonality exhibit a wide range of results, while the meridional distribution of these metrics along selected coastal (but not interior) transects are quite similar across methods. Furthermore, methods are grouped into criteria-based clusters, within which the range of results is reduced. AR case studies and an evaluation of individual method deviation from an all-method mean highlight advantages/disadvantages of certain approaches. For example, methods with less (more) restrictive criteria identify more (less) ARs and AR-related impacts. Finally, this paper concludes with a discussion and recommendations for those conducting AR-related research to consider.

FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

Abstract: FourCastNet, short for Fourier Forecasting Neural Network, is a global data-driven weather forecasting model that provides accurate short to medium-range global predictions at $0.25^{\circ}$ resolution. FourCastNet accurately forecasts high-resolution, fast-timescale variables such as the surface wind speed, precipitation, and atmospheric water vapor. It has important implications for planning wind energy resources, predicting extreme weather events such as tropical cyclones, extra-tropical cyclones, and atmospheric rivers. FourCastNet matches the forecasting accuracy of the ECMWF Integrated Forecasting System (IFS), a state-of-the-art Numerical Weather Prediction (NWP) model, at short lead times for large-scale variables, while outperforming IFS for variables with complex fine-scale structure, including precipitation. FourCastNet generates a week-long forecast in less than 2 seconds, orders of magnitude faster than IFS. The speed of FourCastNet enables the creation of rapid and inexpensive large-ensemble forecasts with thousands of ensemble-members for improving probabilistic forecasting. We discuss how data-driven deep learning models such as FourCastNet are a valuable addition to the meteorology toolkit to aid and augment NWP models.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Nonlinear Time Series Analysis.

Abstract: : This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

Physics-informed machine learning

Abstract: Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Here, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems. The rapidly developing field of physics-informed learning integrates data and mathematical models seamlessly, enabling accurate inference of realistic and high-dimensional multiphysics problems. This Review discusses the methodology and provides diverse examples and an outlook for further developments.

Journal of Fluid Mechanics创刊50周年

Abstract: 流体力学杂志“Journal of Fluid Mechanics”由剑桥大学教授George Batchelor在1956年5月创办，在国际流体力学界享有很高的学术声望，被公认为是流体力学最著名的学术刊物之一，2005年的影响因子为2．061，雄居同类期刊之首．在它创刊50周年之际，2006年5月JFM出版了第554卷的纪念特刊，其中刊登了现任主编（美国西北大学S．H．Davis教授和英国剑桥大学T．J．Pedley教授）合写的述评：“Editorial：JFM at50”，以JFM为背景，从独特的视角对近50年来流体力学的发展进行了简明的回顾和展望，并归纳了一系列非常有启发性的有趣统计数字．2006年7月21日在剑桥大学应用数学和理论物理研究所（DAMTP）举行了创刊50周年的庆祝会．下午2点，JFM的新老编辑和来宾会聚一堂，Pedley教授致开幕词，其后是5个精彩的报告：The mysterious rattleback and its fluid counterpart（Keith Moffatt），Developments in shear instabilities（Patrick Huerre），Falling clouds（Elisabeth Guazzelli），Ecotectural fluid mechanics（Paul Linden），The success of JFM（Herbert Huppert），最后由Davis教授致闭幕词．

Fourier Neural Operator for Parametric Partial Differential Equations

Abstract: The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The Fourier neural operator is the first ML-based method to successfully model turbulent flows with zero-shot super-resolution. It is up to three orders of magnitude faster compared to traditional PDE solvers. Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution.