Search NASASearch

SEARCH · Search NASA

Results for “ORTHOGONAL FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

Challenges and alternatives to empirical orthogonal functions for earth system data

Empirical orthogonal functions (EOFs) applied to gridded Earth system data enables users to diagnose modes of variability with relative ease. Yet, many challenges to interpretation exist such that they must be used with awareness and intention when applied to gridded climate data, especially with large ensembles. Utilizing data from two different Earth system modelling large ensemble frameworks, the Energy Exoscale Earth System Model and the Community Earth System Model, as well as reanalysis data, common EOF pitfalls are summarized and discussed. Challenges include erroneous mode swapping, sign flipping, and the temporal variability of the centers of action. For modes of variability with similar contribution to variance, mode swapping is not uncommon. Sign flipping can occur with almost any mode where the pattern is correct, but the sign is arbitrary. Although the variability of the center of action is not necessarily problematic, it potentially complicates interpretation over multi-century timescales. A wide variety of alternative methods to EOFs exist, but fitness-for-purpose must be evaluated. Additionally, illustrations of alternative methods and examples of proper use are provided. Alternative methods fit into three categories: EOF variants, linear methods, and multilinear methods.

54 ENVIRONMENTAL SCIENCES

Concurrent Inter-Model Spread of Boreal Winter Westerly Jet Meridional Positions Between the Northern and Southern Hemispheres in CMIP6 Models

Here, this study investigates the inter-model spread of climatological extratropical westerly jets in boreal winter, using the historical simulation of 52 Coupled Model Intercomparison Project phase 6 (CMIP6) models from 1851 to 2014. The results show that there is a substantial spread in the latitude of the upper-tropospheric westerly jet across models, characterised by large inter-model standard deviations to both the poleward and equatorward sides of the jet axis, although the multi-model ensemble mean (MME) performs well in simulating meridional position of westerly jets. Furthermore, we detect the consistency of inter-model jet position spread between the Northern and Southern Hemispheres, based on the inter-model empirical orthogonal function (EOF) decomposition and correlation of regional-averaged zonal winds. Specifically, the models that simulate the westerly jets poleward/equatorward relative to the MME position in one hemisphere also tend to simulate the jets poleward/equatorward in the other hemisphere. Accordingly, we define a global jet spread index to depict the concurrence of jet shift in the two hemispheres. The results of inter-model regression analyses based on this index indicate that the models positioning the jets poleward than the MME tend to simulate a wider Hadley Cell, a poleward-shifted Ferrel Cell in the Southern Hemisphere, enhanced precipitation in the subtropics and suppressed precipitation in the tropics, and warmer sea surface temperatures in the subtropics and mid-latitudes. The present results suggest that improving the simulation of jet positions in climate models requires a comprehensive consideration of thermal states in the tropics and subtropics/mid latitudes.

54 ENVIRONMENTAL SCIENCES

Global teleconnections influencing large-scale drought in the United States using SVDI

Understanding recent large-scale drought patterns and the mechanisms producing extreme drought events is vital for future drought forecasts and understanding future drought risks. Increasingly, vapor pressure deficit (VPD) has been used as an important measure of evaporative demand and proxy for drought detection. In this study, VPD is used to calculate the new Standardized VPD Drought Index (SVDI) with NASA North American Land Data Assimilation System (NLDAS) data. Previous studies have shown that SVDI accurately identifies the timing and magnitude short-term droughts in the United States (U.S). In the present study, SVDI is now used to identify large-scale drought patterns between 1980 and 2021 and drought variability driven by selected global teleconnections originating in the Pacific and Atlantic Oceans. Spatial drought characteristics were extracted from SVDI using empirical orthogonal function (EOF) analysis. Then a k-means clustering algorithm was applied to both EOF principal components and primary teleconnections, including the El Nino-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) to identify drought events driven by the Pacific Ocean. Results show that the SVDI is useful in evaluating large-scale drought variability in the U.S. related to global teleconnections, and that mechanisms influencing summer drought patterns in the Western and Southwestern U.S. are driven by a tropical-extratropical interactions originating in the equatorial Pacific Ocean related to ENSO dynamics with interdecadal variability modulated by PDO. The large-scale droughts in the Central and Southern U.S., like those in 2011 and 2012, on the other hand, are driven by the North Pacific Ocean warm pool during a strong negative PDO, which subsequently influenced variability in the Bermuda-Azores High in the Atlantic Ocean. In summer 2011, the Bermuda-Azores High weakened, reducing the onshore winds and moisture transport along the eastern Gulf of Mexico and contributing to ongoing drought in the region. The Northern Pacific and Atlantic Ocean sea surface temperatures (SSTs) have increased between 1980 and 2021. In conclusion, as SSTs continue to rise in the Northern Pacific Ocean, one consequence of the coupled North Pacific warm pool and atmospheric dynamics, is to increase summer drought variability over a large region in the southern and midwestern U.S. under global warming.

54 ENVIRONMENTAL SCIENCES

Numerical Analysis of Offshore Wind-Farm-Induced Drag Effects on Coastal Upwelling Dynamics

Wind farms extract momentum from the atmospheric flow, generating wind-speed deficits both within the plant, and extending downstream. When located offshore, these deficits modulate air-sea coupling, potentially impacting coastal upwelling in sensitive regions. We investigate impacts of wind farms on coastal upwelling using kilometre-scale, three-way-coupled simulations with the coupled ocean-atmosphere-wave-sediment transport system for the US West Coast. Wind-farm effects are represented by a generalised turbine drag formulation, an idealised, height-dependent body force whose magnitude is systematically varied. This approach isolates the leading-order fluid-dynamical response in a realistic coastal configuration. The atmospheric adjustment exhibits an approximately linear relation between drag force and wind-speed deficit, with wakes that expand downstream and increase in magnitude as drag increases. An empirical orthogonal function analysis of sea-surface-temperature anomalies reveals the emergence of a canonical dipole pattern under strong drag forcing. Subsurface diagnostics show consistent shoaling of the mixed layer and suppressed upward velocities in areas near wind-farm region, accompanied by compensating enhancements of shoaling closer to the coast. These results identify turbine drag as a control parameter in assessing interactions between wind-farm wake and coastal upwelling and provide scaling relationships for understanding offshore wind-farm effects on the coastal circulation dynamics.

16 TIDAL AND WAVE POWER

Propagation and Periodicity of Mars's Northern Annular Mode Modulates the Dust Cycle

Abstract We document the propagation of annular modes—zonally symmetric patterns of variability—in Mars's atmosphere using a reanalysis dataset. Mars's Northern Annular Mode (MNAM) sees anomalies of zonal‐mean zonal wind emerge near the subtropics and migrate poleward with a period of 150 days, similarly to Earth's Southern Annular Mode. The mechanism of propagation involves the interaction of the two leading empirical orthogonal functions that define the MNAM. Moreover, the propagation encourages alternating bands of surface wind stress to migrate polewards with a 150‐day period. In addition, a 150‐day periodicity in anomalous column dust optical depth most likely emerges in response to extrema of the MNAM. The combination of the impact of the MNAM's internally forced periodicity on the surface wind stress and the seasonal cycle may contribute to the inter‐annual variability of global dust events, as suggested by a Monte Carlo estimate that correctly approximates the observed incidence of global dust events.

54 ENVIRONMENTAL SCIENCES

OpenCRUMS USA: An Open Machine Learning Framework for Characterizing Variability in Aerosol Reanalysis Data

Advances in artificial intelligence (AI) have called for exploring how these techniques can be used for exploring patterns in large climate datasets. To that regard, the U.S. Department of Energy AI for Earth System Predictability (AI4ESP) supported a pilot initiative called the Open Classification of Regimes in the Southeast USA (OpenCRUMS USA) project to explore how AI can be used to characterize modes of spatial variability in large climate datasets. For this study, we focus on comparing two methods for characterizing the modes of spatial variability of surface aerosol concentration over the Houston region: empirical orthogonal functions (EOFs) and layerwise relevance propagation (LRP) applied to a convolutional neural network (CNN) classifier. We show that EOF analysis typically attributes spatial variability modes that span all of southeast Texas, prohibiting the attribution of spatial variability to localized regions. However, using LRP on the CNN classifier resolves the explanatory parameters at a finer spatial resolution than EOFs. This allows for the attribution of the spatial variability of surface aerosols to local regions of organic carbon which was not possible using EOFs. In addition, the LRP analysis also suggests that synoptic-scale transport of dust is most prevalent during anticyclonic and pretrough synoptic conditions as categorized by self-organizing maps.

54 ENVIRONMENTAL SCIENCES

Investigating the Relative Contribution from Tropical Indo-Pacific SST to Asian Monsoon Precipitation Variability Using LIM

Abstract A critical issue is determining the factors that control the year-to-year variability in precipitation over southern Asia. In this study, we employ a cyclostationary linear inverse model (CS-LIM) to quantify the relative contribution of tropical Pacific and Indian Ocean sea surface temperature anomalies (SSTAs) to the interannual variability of the Asian monsoon, especially Indian summer monsoon rainfall (ISMR). Through a series of CS-LIM experiments, we isolate the impacts of the direct forcing from Pacific SSTAs, Indian Ocean SSTAs, and their interaction on Asian monsoon rainfall variability. Our results reveal distinct patterns of influence with the direct forcing from the Pacific (Indian) Ocean tending to enhance (reduce) the magnitude of precipitation variability, while the Indo-Pacific interaction acts to strongly damp the variability of Asian monsoon precipitation, especially over India. We further investigate these specific impacts on ISMR by analyzing the relationship between tropical Indo-Pacific SSTAs and the leading three empirical orthogonal functions (EOFs) of ISMR. The results from our CS-LIM experiments indicate that the direct forcing from El Niño–Southern Oscillation (ENSO) enhances the variability of the first and third EOFs, while the Indian Ocean SSTA opposes ENSO’s effects, which is consistent with previous studies. Our new results show that the tropical Indo-Pacific interaction strongly damps ISMR variability, which is due to the ENSO-induced Indian Ocean dipole (IOD) opposing the direct impacts from ENSO on ISMR. Additionally, reduced ENSO amplitude and duration associated with the Indo-Pacific interaction may also contribute to the damping effect on ISMR, but this requires further study to understand the relevant mechanisms.

Meteorology & Atmospheric Sciences

Weak Form Scientific Machine Learning: Test Function Construction for System Identification

Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions. In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creating the set of test functions. Our approach numerically approximates the integration error introduced by the quadrature and identifies the support size for which the error is minimal, without requiring access to the model parameter values. Through numerical experiments across various models, noise levels, and temporal resolutions, we demonstrate that the selected supports consistently align with regions of minimal parameter estimation error. We also compare the proposed method against the strategy for constructing Multi-scale-Global (and orthogonal) test functions introduced in our prior work, demonstrating the improved computational efficiency.

FOS: Computer and information sciences

The effective number of parameters in kernel density estimation

We devise a new formula for measuring the effective degrees of freedom (EDoF) in kernel density estimation (KDE). Starting from the orthogonal polynomial sequence (OPS) expansion for the ratio of the empirical to the oracle density, we show how convolution with the kernel leads to a new OPS with respect to which one may express the resulting KDE. The expansion coefficients of the two OPS systems can then be related via a kernel sensitivity matrix, which leads to a natural oracle definition of EDoF through the trace operator. Asymptotic properties of the (empirical) plug-in EDoF are worked out through influence functions, and connections with other empirical EDoFs are established. Minimization of Kullback-Leibler divergence is investigated as an alternative to integrated squared error based bandwidth selection rules, yielding a new normal scale rule. The methodology, which arises from a proper oracle formulation and is not restricted to convolution kernels, suggests the possibility of a new bandwidth selection rule based on an information criterion such as AIC.

bandwidth selection

Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

97 MATHEMATICS AND COMPUTING

Engineering modular enzyme assembly: synthetic interface strategies for natural products biosynthesis applications

Covering: 2020 to 2025Natural products remain indispensable sources of therapeutic and bioactive compounds, yet traditional discovery strategies are constrained by compound rediscovery. Modular biosynthetic enzymes, such as type I polyketide synthases (PKSs) and type A non-ribosomal peptide synthetases (NRPSs), offer promising platforms for combinatorial biosynthesis owing to their programmable architectures. However, practical implementation is frequently limited by inter-modular incompatibility and domain-specific interactions. This review highlights recent advances in modular enzyme assembly enabled by synthetic interfaces-including cognate docking domains, synthetic coiled-coils, SpyTag/SpyCatcher, and split inteins-which function as orthogonal, standardized connectors to facilitate post-translational complex formation. These interfaces support rational investigations into substrate specificity, module compatibility, and pathway derivatization as well as general enzyme clustering applications beyond PKS and NRPS systems. Synthetic interfaces can be integrated with computational tools to support a more systematic and scalable framework for modular enzyme engineering by providing predictive insights into domain compatibility and interface design. These approaches within iterative design-build-test-learn workflows can accelerate the programmable assembly of biosynthetic systems and expand the accessible chemical space for natural products.

Kim, Gahyeon

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion

The overlapping fragment approach for non-orthogonal configuration interaction with fragments

The non-orthogonal configuration interaction with fragments (NOCI-F) approach is extended opening the possibility to study intramolecular processes and materials with covalent or ionic lattices. So far, NOCI-F has been applied to study intermolecular energy and electron transfer employing ensembles of fragments that do not have atoms or bonds in common. The here presented approach divides the target system into two overlapping fragments that share one or more atoms and/or one or more bonds. After the construction of a collection of (multiconfigurational) fragment wave functions in a state specific optimization procedure, the fragment wave functions are combined to form many-electron basis functions for the non-orthogonal configuration interaction of the whole system. The orbitals in the overlapping fragment are defined by a corresponding orbital transformation of the fragment orbitals through a singular value decomposition. The overlapping fragments approach is first illustrated for a model system and then used to highlight some possible applications of NOCI with overlapping fragments. In conclusion, the results of excited state diffusion in transition metal oxide, intramolecular singlet fission and magnetic interactions in organic biradicals and ionic compounds are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Identifying Hot Spots and Hot Moments of Metabolic Activity in Salt Marsh Sediments through BONCAT-FISH Microscale Mapping (Final Technical Report)

Understanding the biogeography and timing of microbial metabolic activity is a key priority for microbial ecologists. With such knowledge, the cumulative biogeochemical contributions of microbial communities become more predictable, and our ability to both understand the effects of environmental change on microbial activity and build synthetic communities with desired functions will increase substantially. In this project, we advanced this broad, ambitious goal in two substantial ways: we developed a multiplexed Fluorescence In Situ Hybridization (FISH) approach that links microbial identity with metabolic function, and we established a novel Bio-Orthogonal Non-Canonical Amino acid Tagging (BONCAT) technique that can resolve the timing of anabolic activity, providing new resolution of when microbial constituents are growing. We deployed both of these techniques in multiple environmental settings to demonstrate their versatility. At the Little Sippewissett Salt Marsh, we combined a novel dual-BONCAT technique with fluorescence activated cell sorting to determine which population of cells was metabolically active during the day and which was active during the night. We found that Methylobacterium was active during daylight hours, potentially feeding on carbon-rich molecules released from plant roots. Sulfur-cycling microbes dominate the population active during the dark night-time hours. Overall, the work conducted under the auspices of this project developed two promising new techniques for identifying the “hot spots” and “hot moments” of microbial activity in complex communities with taxonomic and functional resolution. We focused largely on a salt marsh sediment context, but are confident that microbial ecologists seeking to understand the microbial role in biogeochemical cycles in a wide range of settings will find our newly developed techniques useful in future work.

54 ENVIRONMENTAL SCIENCES

Supersymmetric Virasoro minimal strings

A random matrix model definition of a family of N = 1 supersymmetric extensions of the Virasoro minimal string of Collier, Eberhardt, Mühlmann, and Rodriguez is presented. An analysis of the defining string equations shows that the models all naturally have unambiguous nonperturbative completions, which are explicitly supplied by the double-scaled orthogonal polynomial techniques employed. Perturbatively, the multiloop correlation functions of the model define a special supersymmetric class of “quantum volumes,” generalizing the prototype case, some of which are computed. Published by the American Physical Society 2024

Astronomy & Astrophysics

RNAi and genome editing of sugarcane: Progress and prospects

SUMMARY Sugarcane, which provides 80% of global table sugar and 40% of biofuel, presents unique breeding challenges due to its highly polyploid, heterozygous, and frequently aneuploid genome. Significant progress has been made in developing genetic resources, including the recently completed reference genome of the sugarcane cultivar R570 and pan‐genomic resources from sorghum, a closely related diploid species. Biotechnological approaches including RNA interference (RNAi), overexpression of transgenes, and gene editing technologies offer promising avenues for accelerating sugarcane improvement. These methods have successfully targeted genes involved in important traits such as sucrose accumulation, lignin biosynthesis, biomass oil accumulation, and stress response. One of the main transformation methods—biolistic gene transfer or Agrobacterium ‐mediated transformation—coupled with efficient tissue culture protocols, is typically used for implementing these biotechnology approaches. Emerging technologies show promise for overcoming current limitations. The use of morphogenic genes can help address genotype constraints and improve transformation efficiency. Tissue culture‐free technologies, such as spray‐induced gene silencing, virus‐induced gene silencing, or virus‐induced gene editing, offer potential for accelerating functional genomics studies. Additionally, novel approaches including base and prime editing, orthogonal synthetic transcription factors, and synthetic directed evolution present opportunities for enhancing sugarcane traits. These advances collectively aim to improve sugarcane's efficiency as a crop for both sugar and biofuel production. This review aims to discuss the progress made in sugarcane methodologies, with a focus on RNAi and gene editing approaches, how RNAi can be used to inform functional gene targets, and future improvements and applications.

Brant, Eleanor [Agronomy Department, Plant Molecul