Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 30 October 2019Accepted: 19 January 2021Published online: 17 May 2021Keywordsmixed precision, fp16, QR factorization, rounding error, block QR, fp32AMS Subject Headings65G50, 65F25, 65F08, 65F10Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industrial and Applied MathematicsCODEN: sjoce3

Machine learning for the parameterization of subgrid-scale processes in climate models has been widely researched and adopted a few models. A key challenge developing data-driven schemes is how to properly represent rare, but important events that occur geoscience datasets. We investigate develop strategies reduce errors caused by insufficient sampling rare data regime, under constraints no new further expansion model complexity. Resampling importance weighting are constructed with user...

Abstract Two key challenges in the development of data‐driven gravity‐wave parameterizations are generalization, how to ensure that a scheme trained on present‐day climate will continue work new regime, and calibration, account for biases “host” model. Both problems depend fundamentally response out‐of‐sample inputs compared with training dataset, often conflicting. The ability generalize regimes goes hand sensitivity model biases. To probe these challenges, we employ one‐dimensional (1D)...

Abstract The ensemble forecast dominates the computational cost of many data assimilation methods, especially for high‐resolution and coupled models. In situations where is prohibitive, one can either use a lower‐cost model or method, both. Ensemble optimal interpolation (EnOI) classical example method that replaces with single then constructs an about this by adding perturbations drawn from climatology. This research develops methods add to forecast, are obtained analogs forecast. These be...

We explore the various ways rounding errors can impact power method for calculating Fielder vector graph clustering. A error analysis reveals that best eigenpair is computable with a certain floating point precision type has worst-case scales to its unit round-off. Although accumulate in at bound, this behavior not reflected some practical examples. Furthermore, our numerical experiments show from may satisfy conditions necessary bounding of mis-clustering rate and approximate eigenvectors...

Summary A new optimal staggered-grid finite difference (SFD) scheme based on minimax approximation method is proposed to perform high accuracy numerical solution. Optimal SFD coefficients can be determined by using Remez algorithm under the iterative condition of Chebyshev's criteria better approximate first-order spatial derivatives. Numerical analysis shows that provide at large wavenumber for same operator length, compared with conventional Taylor-series expansion coefficients....

Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing in employing computations motivates need rounding error analysis that properly handles behavior arithmetic. We develop variants of existing Householder QR algorithms show analyses supported by numerical experiments.

<p>An essential step in implementing any new parameterization is calibration, where the adjusted to work with an existing model and yield some desired improvement. In context of gravity wave (GW) momentum transport, calibration necessitated by facts that: (i) Some GWs are always at least partially resolved model, hence a should only account for missing waves. Worse, may need correct misrepresentation under-resolved GWs, i.e., coarse vertical resolution can bias GW breaking...

<p>With the goal of developing a data-driven parameterization unresolved gravity waves (GW) momentum transport for use in general circulation models (GCMs), we investigate neural network architectures that emulate Alexander-Dunkerton 1999 (AD99) scheme, an existing physics-based GW parameterization. We analyze distribution errors as functions shear-related metrics effort to diagnose disparity between online and offline performance trained emulators, develop sampling algorithm...

<p>We propose to use analogs of the forecast mean generate an ensemble perturbations for in optimal interpolation (EnOI) or variational (EnVar) methods.  In addition finding from a library, we new method constructing using autoencoders (a machine learning method).  To extend scalability constructed data assimilation on geophysical models, patching schemes divide global spatial domain into digestable chunks.  Using patches makes training...