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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains, from electrostatics to porous media flow. Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures. Machine learning-based approaches address this by replacing iterative solving processes with one-time inference; however, their sophisticated models require extensive training resources that often exceed those of traditional solvers. Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge. In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DEs) to efficiently and accurately solve TIDEs. DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibrium -- the solution of the target TIDE -- within ~1µs on a ~1-watt DS-TIDE processor. To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -- conditioning, solving, and decoding -- each governed by specialized dynamics. The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations. Furthermore, DS-TIDE is equipped with an on-device DS-DE Auto-Alignment mechanism that dynamically adapts intrinsic hardware dynamics within milliseconds, effectively aligning the system’s dynamics to diverse target DEs. Experimental results across TIDEs from a wide range of scientific and engineering domains demonstrate that DS-TIDE achieves ~10^3× speedup, ~10^5× energy savings, and competitive or superior accuracy compared to state-of-the-art numerical and ML-based solvers.

Liu, Chuan↗
DOE OSTI2024

Implementing Superresolution of Nonstationary Tides with Wavelets: An Introduction to CWT_Multi

Abstract Tides are often nonstationary due to nonastronomical influences. Investigating variable tidal properties implies a trade-off between separating adjacent frequencies (using long analysis windows) and resolving their time variations (short analysis windows). Previous continuous wavelet transform (CWT) tidal methods resolved tidal species. Here, we present CWT_Multi, a MATLAB code that 1) uses CWT linearity (via the “response coefficient method”) to implement superresolution, i.e., resolving tidal constituents beyond the Rayleigh criterion; 2) provides a Munk–Hasselmann constituent selection criterion appropriate for superresolution; and 3) introduces an objective, time-variable form of inference (“dynamic inference”) based on time-varying data properties. CWT_Multi resolves tidal species on time scales of days, and multiple constituents per species with fortnightly filters. It outputs astronomical phase lags and admittances, analyzes multiple records, and provides power spectra of the signal(s), residual(s), and reconstruction(s); confidence limits; and signal-to-noise ratios. Artificial data and water levels from the Lower Columbia River Estuary (LCRE) and San Francisco Bay Delta (SFBD) are used to test CWT_Multi and compare it to harmonic analysis programs NS_Tide and UTide. CWT_Multi provides superior reconstruction, detiding, dynamic analysis utility, and time resolution of constituents (but with broader confidence limits). Dynamic inference resolves closely spaced constituents (like K 1 , S 1 , and P 1 ) on fortnightly time scales, quantifying impacts of diel power peaking (with a 24-h period, like S 1 ) on water levels in the LCRE. CWT_Multi also helps quantify the impacts of high flows and a salt barrier closing on tidal properties in the SFBD. On the other hand, CWT_Multi does not excel at prediction, and results depend on analysis details, as for any method applied to nonstationary data. Significance Statement Ocean tides, especially in coastal and estuarine systems, are often nonstationary, in the sense that the mean and standard deviation of tidal properties vary over time, usually in response to some nontidal process. We introduce here a MATLAB code, CWT_Multi, that uses wavelet transforms to resolve both tidal species and constituents on time scales from a few days to months. Our code accommodates multiple scalar time series and has typical tidal analysis features like constituent selection and inference, plus two forms of uncertainty analyses. It is flexible, allowing the user to adapt analysis properties to diverse datasets. CWT_Multi is applicable to many problems involving time-variable tides, including sea level rise, compound flooding, sediment transport, and wetland habitat analyses. Application to vector data is a straightforward extension, but further development of our uncertainty analysis is merited. Because nonstationary tidal analysis is rapidly advancing, we also define the features of a “well-formed” analysis code.

Lobo, Matthew↗
DOE OSTI2025

15-minute Parker River gap-filled tide height and salinity data, PIE LTER, Plum Island Sound, MA (2014–2023), for ELM PFLOTRAN modeling

This dataset contains 15-minute tide height and salinity data from the Typha site along the Parker River, part of the Plum Island Ecosystems Long Term Ecological Research (PIE LTER) site in Plum Island Sound, Massachusetts (MA) 2014-2023. Tide height (in NAVD88) was compiled from measurements conducted at the mouth of Plum Island Sound and corrected for time lags. Gap-filling of missing periods were done by fitting tidal constituents to the time series. Salinity was measured (and is stored on ESS DIVE ) in 2022 and 2023 using HOBO U24-002 conductivity loggers. River discharge is the most important control on tidal river water salinity at the location (Vallino & Hopkinson, 1998). An artificial neural network was trained to predict river water salinity at the location using Parker River discharge (USGS station 01101000, Parker River at Byfield, MA) and gap-filled salinity observations from a long-term monitoring station ca. 3km downstream from the Typha site (LTER station ‘Middle Road’) as input variables to create continuous time series information. The data set was used in the spin up and simulations of a land surface model coupled to a biogeochemical reaction network (ELM PFLOTRAN) assessing impacts of hydrology and salinity input on methane fluxes in 2022 and 2023 (Sulman et al., 2024). Metadata files ELMPFLOTRAN_tide_salinity_dd.csv and ELMPFLOTRAN_tide_salinity_flmd.csv provide details on site location, data variables, and QA/QC methods .

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

From tides to seasons: How cyclic tidal drivers and plant physiology interact to affect carbon cycling at the terrestrial-estuarine boundary (Final technical report)

Coastal ecosystems are among the most biologically and biogeochemically active and diverse systems on Earth. Because they act as important linkages between terrestrial ecosystems and the open ocean, their incorporation in Earth system models (ESMs) is critical to predict coastal and global responses to environmental changes. However, they vary greatly in the magnitude of tides and the volume and timing of freshwater input from land, making it challenging to model the major biogeochemical reactions that control productivity and greenhouse gas emissions across coastal terrestrial aquatic interfaces (TAIs). Our overall objective was to improve mechanistic process understanding and modeling of tidal wetland hydro-biogeochemistry in coastal TAIs. We established a new flux tower site (Ameriflux US-PLo) in the oligohaline part of the Parker River to continuously monitor ecosystem-scale carbon fluxes under temporally varying salinity conditions. The site is co-located with long-term monitoring plots of the Plum Island Ecosystems LTER project. We installed wells and redox sensors in the marsh interior and creek bank, established biomass monitoring plots and deployed novel optode sensors in both locations. We used this data to parameterize plant-mediated transport in PFLOTRAN and tested the impact of soil heterogeneity on porewater constituents and gas fluxes. We collected observations of root oxygen release with a novel planar optode system in the field. Flux data collected during the measurement period encompasses a large variation in salinity ranging from drought to record precipitation years. We developed a method to extract functional relationships from the flux data using artificial neural networks, identifying salinity thresholds for CH 4 fluxes. Finally, we are using the coupled ELM-PFLOTRAN model to test the impact of antecedent hydrological conditions on the salinity-CH 4 flux relationship. This grant contributed to the professional development of one postdoc, three research assistants and one graduate student. The sensor data has been shared with external collaborators.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Golden Tide Opportunities

There is no abstract for this document. I have been invited to present my project progress to the Schmidt Sciences VIFF SaBRe team at their annual project meeting. This is work funded by DOE AFFO. The project title is Algal Feedstock Logistics

09 - BIOMASS FUELS↗
DOE OSTI2025

Decomposing a Compound Flood Event in an Urban Pacific Northwest Estuary: Primary Drivers and Projections for the Future

The Duwamish River Estuary (DRE) of Washington is prone to compound flooding during atmospheric river (AR) events. The processes contributing to such flooding (coastal and fluvial) have remained opaque to municipalities that are increasingly impacted. Here, we conduct a suite of coupled atmosphere-hydrology-ocean model simulations with varying forcing combinations (tide, surge, and/or river discharge) to identify the primary drivers of compound flooding during a recent AR event. We also test year 2,100 climate forcing to project how flooding and drivers may change in the future for the same event. We identify a clear distinction between dynamics in the downstream, engineered portion of the DRE compared to the upstream, “natural” river. Downstream, tides dominate water levels but contributions from storm surge and nonlinear tide-surge interaction elevate tide-only high waters from no flooding to major flooding. Upstream, total water levels during the event are ∼6 cm higher than downstream due to an increasing influence of river discharge over surge and tides. Notably, nonlinear surge-river and tide-river interactions act to reduce upstream water levels up to 50% compared to estimates which linearly sum tides, surge, and river, likely reducing flood vulnerability. Under two future climate scenarios: one with only sea level rise (SLR) and another with SLR plus atmospheric warming, we find little change in mechanism contributions to water levels. Expanded flooding in both cases is largely due to SLR, as a ∼50% increase to river discharge under the warming scenario has no impact downstream and marginally increases (∼3 cm) water level upstream.

atmospheric river↗
DOE OSTI2025

Spatially varying seasonal modulation to tidal stream energy potential due to mixed tidal regimes in the Aleutian Islands, AK

We provide an assessment of the tidal stream energy resource of the Aleutian Islands, Alaska via a validated barotropic tidal numerical model of the region. Eight island passes are identified as energy “hotspots”. The annual mean kinetic energy fluxes, KEF , calculated at each pass vary from 1000 to 11,000 MW, while the annual available energy, AAE , varies from 5 to 42 MWh m −2 . Notable seasonal modulation to monthly power density averages and ranges are noted at some passes and not others. Seasonal adjustment is linked to the semi-annual solar declination cycle which enhances (dampens) diurnal (D 1 ) tidal amplitudes in summer/winter (spring/fall) as well as the time-varying phase lag between D 1 and semidiurnal (D 2 ) fortnightly tidal cycles. Annual variability in monthly mean power density scales with the tidal current form factor, F u , with the largest seasonal change occurring for F u > 1 (D 1 dominated tide). The spread in power density over a month is on average smaller for passes with mixed tides (F u = 1 ) than those with D 1 or D 2 dominance, as changes to fortnightly phase lag become influential to net power density ranges when tides are mixed. This study outlines overlooked, but relevant, long-term modulation to tidal streams in regions with mixed tides.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Uncertainty-Guided Prediction Horizon of Phase-Resolved Ocean Wave Forecasting Under Data Sparsity: Experimental and Numerical Evaluation

Accurate short-term wave forecasting is critical for the safe and efficient operation of marine structures that rely on real-time, phase-resolved ocean wave information for control and monitoring purposes (e.g., digital twins). These systems often depend on environmental sensors (e.g., waverider buoys, wave-sensing LIDAR). Challenges arise when upstream sensor data are missing, sparse, or phase-shifted due to drift. This study investigates the performance of two machine learning models, time-series dense encoder (TiDE) and long short-term memory (LSTM), for forecasting phase-resolved ocean surface elevations under varying degrees of data degradation. We introduce the τ-trimming algorithm, which adapts the prediction horizon based on uncertainty thresholds derived from historical forecasts. Numerical wave tank (NWT) and wave basin experiments are used to benchmark model performance under short- and long-term data masking, spatially coarse sensor grids, and upstream phase shifts. Results show under a 50% probability of upstream data loss, the τ-trimmed TiDE model achieves a 46% reduction in error at the most upstream target, compared to 22% for LSTM. Furthermore, phase misalignment in upstream data introduces a near-linear increase in forecast error. Under moderate model settings, a ±3 s misalignment increases the mean absolute error by approximately 0.5 m, while the same error is accumulated at ±4 s using the more conservative approach. These findings inform the design of resilient, uncertainty-aware wave forecasting systems suited for realistic offshore sensing environments.

42 ENGINEERING↗
DOE OSTI2025

A cross-dimensional analysis of data-driven short-term load forecasting methods with large-scale smart meter data

Electricity load forecasting is essential to utility operation and power grid stability. A wide spectrum of data-driven methods, ranging from linear regression models to more recent deep learning models have been adopted to forecast electric load over the years. However, there still lacks a holistic evaluation of the applicability of conventional statistical and machine learning based algorithms with respect to different temporal and spatial scopes, computational requirements, and sensitivity of model-tuning. Enabled by a large-scale electricity load profile dataset of over 40,000 residential customers in a utility region, we conducted a cross-dimensional analysis of data-driven load forecasting methods. Three regression-based and seven deep learning algorithms with different model configurations were evaluated in terms of their overall and peak load prediction accuracy, and training burdens, across spatial aggregation levels ranging from the transformer, feeder, substation, to neighborhood. We found, first, the load forecasting accuracy is constrained by a predictability boundary, influenced by the forecasting horizon and spatial aggregation level. Specifically, RandomForest, XGBoost, TFT, TSMixer, and TiDE models achieved less than 10 % prediction error for up to 96-h ahead forecasting for district, substation, and feeder levels, while other models struggle at long-horizon predictions; Second, for winter and summer peak load dates, most models were able to predict the peak demand timing within ± 1 h, but the prediction percentage error varied by models, with TFT and TiDE models being the top performers; Third, models with similar prediction accuracy can differ in training burden by an order of magnitude. Therefore, choosing model configurations that balance prediction performance and computational resource is an important practical consideration for large-scale deployment of the machine learning based load forecasting. The outcome of this study can guide researchers and practitioners to choose the proper load forecasting algorithms based on their problem scope, required accuracy, and available resources. The predictability boundary can serve as a benchmark for electricity load forecasting problems with new algorithms and datasets.

Li, Han↗
DOE OSTI2025

Forecasting Multi-Step-Ahead Street-Scale Nuisance Flooding using a seq2seq LSTM Surrogate Model for Real-Time Application in a Coastal-Urban City

In coastal-urban cities facing an elevated risk of nuisance flooding (by rain and tide) due to increased heavy rainfall, sea level rise, urbanization, and aging drainage systems, real-time flood forecasting at the street-scale can provide useful information to transportation decision-makers. Physics-Based Models (PBMs) that offer high accuracy come with high computational runtimes and costs that limit their application for real-time flood forecasting. To address this challenge, Machine Learning (ML) surrogate models trained from PBMs have been proposed to provide street-scale flood forecasts. Previous related studies have focused on using Long Short-Term Memory (LSTM) architectures to model hourly flood depth on streets. While LSTM models can capture input sequences effectively, they fall short in accurately preserving output sequences, limiting their suitability for multi-step-ahead forecasts. The seq2seq LSTM architecture offers a key advantage here by capturing the full sequence of input–output, making it potentially more suitable for multi-step-ahead flood forecasts compared to traditional LSTM models. However, seq2seq LSTM has not been tested for street-scale flood forecasting, particularly for rapidly fluctuating nuisance flooding events which require special attention to its temporal sequences. Hence, in this study, we applied the seq2seq LSTM model to explore multi-step-ahead street-scale nuisance flooding and compared its results to the traditional LSTM model as a benchmark model. LSTM and seq2seq LSTM surrogate models were applied to 22 flood-prone streets in Norfolk, Virginia, as a case study with a 4-hr (short-term) and 8-hr (long-term) lead time. The models were trained with environmental (rainfall and tide) and topographic (elevation, Topographic Wetness Index, and Depth-To-Water) features along with PBM-derived water depths for different storm events. The results demonstrated satisfactory performance of both LSTM and seq2seq LSTM surrogate models throughout the forecast period compared to the PBM. However, the seq2seq LSTM showed lower Mean Absolute Error (MAE)/ Root Mean Square Error (RMSE) and higher Nash–Sutcliffe Efficiency (NSE)/ correlation than the LSTM across most lead times, particularly for long-term forecasting due to its supremacy in handling both input–output sequences together, which is missing in the traditional LSTM. For example, in the long-term, the average RMSE ranges were 0.0268–0.0373 m for LSTM and 0.0226–0.0319 m for seq2seq LSTM, while in the short-term, they were 0.0263–0.0293 m and 0.0261–0.0283 m, respectively. Additionally, while both models exhibited similar performance in distinguishing flooded and non-flooded streets for flood depth ≥ 0.1 m, the seq2seq LSTM model demonstrated superior performance for higher flood depths (such as ≥ 0.2 m and ≥ 0.3 m). Once trained, inference took only 0.09 to 0.11 s (short-term) and 0.30 to 0.35 s (long-term) per storm event for the 22 streets, making the application highly suitable for real-time decision-making during nuisance flood events.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Tidal energy resource characterization measurements at Cook Inlet’s East Foreland: Velocity and turbulence

To characterize tidal current and turbulence at a top tidal energy site off the East Foreland in Cook Inlet, Alaska, United States, three moorings were deployed for two months between July and August 2021, and a transect survey was conducted over the course of two tidal cycles at the end of the deployment period. Measurements of velocity and turbulence were then analyzed to better understand the site's hydrodynamics and power potential. Analysis reveals that swift, north-flowing flood currents peak at 4~m/s, while south-flowing ebb currents reach just over 3~m/s. Turbulence intensity ranges from 23\% at the seafloor to 8\% near the surface, and the presence of the foreland creates more intense turbulence near-shore during ebb tide than flood. Power availability at the site could be as high as 720~MW, or 13~kW/m$^2$, though the energy available to a marine energy device will be smaller than this estimate because of water-to-wire efficiency and wake losses. The results from this measurement campaign will inform the validation of a high-resolution tidal hydrodynamic model, as well as early tidal energy projects that are beginning to move beyond the prototyping and demonstration stages to full-scale deployments.

McVey, James R.↗
DOE OSTI2025

Pan-Pacific low-frequency modes of sea level and climate variability

Tide gauges provide a long observational record that can inform the nature of satellite-era basin-scale sea level trends. However, common signals must be extracted from geographically sparse records. Here, by applying low-frequency component analysis (LFCA) to tide gauge records and surface climate reconstructions, we isolate three coherent modes of Pacific Ocean variability that we ascribe to: a secular, greenhouse gas–driven climate change (LFC1); a nonlinear mode of variability with a reversal around 1980, potentially linked to aerosols (LFC2); and the Interdecadal Pacific Oscillation (LFC3). Although sea level trend patterns reflect the superimposed contribution of all modes, satellite-era trends are dominated by an increasing phase of LFC2: They are thus potentially unrepresentative of both longer-term historical patterns and those expected in the future.

Science & Technology - Other Topics↗
DOE OSTI2025

Near Resonance between the Shelf Ocean and Semidiurnal Atmospheric Tidal Winds

This manuscript illustrates the resonance between continental shelf oceans and the semidiurnal atmospheric tidal wind, explaining O(10 −2 ) m semidiurnal sea surface height (SSH) variations in detided datasets. The resonance, similar to amplification of semidiurnal oceanic tides on the gentle and wide shelf, results in pronounced, offshore-attenuated standing waves on the shelf which is driven by the cross-shore pressure gradient force, Coriolis force, and the rotary wind stress. Observations and numerical results from the Texas–Louisiana shelf confirm this mechanism, where a significant presence of the semidiurnal tidal wind couples with O(10 −1 ) m s −1 ocean currents, influencing SSH distribution and sustaining the wave structure. The consistency of the interaction and momentum budgets with the analytical solution suggests the robustness of the semidiurnal atmospheric tidal wind interacting with the shelf ocean. Notably, these findings suggest that similar resonances could occur on other gentle shelves known for enhancing semidiurnal oceanic tides and contribute 3%–10% of the wind work.

Atmosphere-ocean interaction↗
DOE OSTI2025

ELM model simulations of Plum Island Ecosystems LTER low marsh site 2018-2020

Model simulations using the Department of Energy's Energy Exascale Earth System Model (E3SM) land model (ELM) with improved capabilities to represent vegetation response to salinity and inundation. The simulations were conducted for a tidal salt marsh at Plum Island Ecosystems Long Term Ecological Research (LTER) site near Rowley, Massachusetts, USA; the site is a low marsh dominated by Spartina alterniflora. The model was forced with site-specific meteorology, salinity and tidal cycles from 2018-2020. Four sets of model simulations are included and described below:1. Parameterization of the salinity response function. These simulations tested different combinations of values for optimal salinity and salinity tolerance.2. Model evaluation. This comparison conducted simulations using the default model, the salinity function only, the submergence function only, and both the salinity and submergence functions. 3. Salinity scenarios. These simulations used the 2018 salinity input data varied by -5 to +10 ppt salinity.4. Water level scenarios. These simulations used the tide height varied by -10 to +50 cm. These simulations were used to demonstrate how the salinity and submergence functions better represent carbon uptake by tidal salt marshes.The data package includes netCDF files used as forcing files for tide height and salinity, one for each year 2018-2020 at observed salinity concentrations, and an additional three forcing files in which salinity concentrations were varied 5 ppt lower, 5 ppt higher, and 10 ppt higher than the measured 2018 time series. Also included are python scripts for creating forcing files, plain text parameter and command files for running simulations, model outputs in netCDF format, and python scripts for visualizing outputs. Code for the modified E3SM model is archived in Sulman et al 2023 at doi:10.15485/1991625. More detail about files is provided in the README.md file.

54 ENVIRONMENTAL SCIENCES↗