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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Non-conservation and conservation for different formulations of moist potential vorticity

Potential vorticity (PV) is one of the most important quantities in atmospheric science. In the absence of dissipative processes, the PV of each fluid parcel is known to be conserved, for a dry atmosphere. However, a parcel's PV is not conserved if clouds or phase changes of water occur. Recently, PV conservation laws were derived for a cloudy atmosphere, where each parcel's PV is not conserved but parcel-integrated PV is conserved, for integrals over certain volumes that move with the flow. Hence a variety of different statements are now possible for moist PV conservation and non-conservation, and in comparison to the case of a dry atmosphere, the situation for moist PV is more complex. Here, in light of this complexity, several different definitions of moist PV are compared for a cloudy atmosphere. Numerical simulations are shown for a rising thermal, both before and after the formation of a cloud. These simulations include the first computational illustration of the parcel-integrated, moist PV conservation laws. The comparisons, both theoretical and numerical, serve to clarify and highlight the different statements of conservation and non-conservation that arise for different definitions of moist PV.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Neural entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws

We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined numerical discretization. While recent neural network architectures have successfully integrated classical numerical principles into learned models, most rely on prior knowledge of the governing equations or assume a fixed discretization. Our approach removes this dependency by embedding entropy-stable design principles into the learning process itself, enabling the discovery of physically consistent dynamics in a fully data-driven setting. By jointly learning both the flux function and a corresponding entropy, NESCFN promotes conservation and entropy dissipation, which is critical for long-term stability and fidelity in the system of hyperbolic conservation laws. Furthermore, numerical results demonstrate that the method achieves stability and conservation over extended time horizons and accurately captures shock propagation speeds, even without oracle access to future-time solution profiles in the training data.

Conservative flux form↗
DOE OSTI2026

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Strategies for conservative and non-conservative monotone remapping on the sphere

Abstract. Monotonicity is an important property of remapping operators for coupled weather and climate models. However, it is often challenging to design highly accurate operators that avoid the generation of new extrema or keep a remapped field between physically prescribed bounds. To that end, this paper explores several traditional and novel approaches for both conservative and non-conservative monotone remapping on the sphere. The accuracy and effectiveness of these algorithms are evaluated in the context of several different real and idealized fields and meshes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Truly conserving with conservative remapping methods

Abstract. Conservative mapping of data from one horizontal grid to another should preserve certain integral or mean properties of the original data. This may be essential in some model applications, including ensuring realistic exchange of energy and mass between coupled model components. It can also be essential for certain types of analysis, such as evaluating how far a system is from an equilibrium state. For some common grids, existing remapping algorithms may fail to perfectly represent the shapes and sizes of grid cells, which leads to errors in the remapped fields. A procedure is presented here that enables users to rely on the mapping weights generated by remapping algorithms but corrects for their deficiencies. With this procedure, for a given pair of source and destination grids, a single set of remapping weights can be applied to remap any variable, including those with grid cells that are partially or fully masked.

58 GEOSCIENCES↗
DOE OSTI2024

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Here, we use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete local energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Local Macroscopic Conservative (LoMaC) Low Rank Tensor Method for the Vlasov Dynamics

Abstract In this paper, we propose a novel Local Macroscopic Conservative (LoMaC) low rank tensor method for simulating the Vlasov-Poisson (VP) system. The LoMaC property refers to the exact local conservation of macroscopic mass, momentum and energy at the discrete level. This is a follow-up work of our previous development of a conservative low rank tensor approach for Vlasov dynamics ( arXiv:2201.10397 ). In that work, we applied a low rank tensor method with a conservative singular value decomposition to the high dimensional VP system to mitigate the curse of dimensionality, while maintaining the local conservation of mass and momentum. However, energy conservation is not guaranteed, which is a critical property to avoid unphysical plasma self-heating or cooling. The new ingredient in the LoMaC low rank tensor algorithm is that we simultaneously evolve the macroscopic conservation laws of mass, momentum and energy using a flux-difference form with kinetic flux vector splitting; then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables by a conservative orthogonal projection. The algorithm is extended to the high dimensional problems by hierarchical Tuck decomposition of solution tensors and a corresponding conservative projection algorithm. Extensive numerical tests on the VP system are showcased for the algorithm’s efficacy.

Guo, Wei↗
DOE OSTI2022

Using a Multi‐Institutional Ensemble of Watershed Models to Assess Agricultural Conservation Effectiveness in a Future Climate

This study investigates the combined impacts of climate change and agricultural conservation on the magnitude and uncertainty of nutrient loadings in the Maumee River Watershed, the second-largest watershed of the Laurentian Great Lakes. Two scenarios — baseline agricultural management and increased agricultural conservation — were assessed using an ensemble of five Soil and Water Assessment Tools driven by six climate models. The increased conservation scenario included raising conservation adoption rates from a baseline of existing conservation practices to feasible rates in the near future based on farmer surveys. This increased adoption of winter cover crops on 6%–10% to 60% of cultivated cropland; subsurface placement of phosphorus fertilizers on 35%–60% to 68% of cultivated cropland; and buffer strips intercepting runoff from 29%–34% to 50% of cultivated cropland. Increased conservation resulted in statistically significant (p ≤ 0.05) reductions in annual loads of total phosphorus (41%), dissolved reactive phosphorus (18%), and total nitrogen (14%) under the highest emission climate scenario (RCP 8.5). While nutrient loads decreased with increased conservation relative to baseline management for all watershed models, different conclusions on the true effectiveness of conservation under climate change may be drawn if only one watershed model was used.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Further adoption of conservation tillage can increase maize yields in the western US Corn Belt

Conservation tillage can reduce soil erosion, increase soil health, and decrease labor and fuel input costs. Despite these benefits, potential yield impacts remain an important concern for farmers considering adoption. Previous research suggests that conservation tillage is likely to have the largest yield benefits in more arid conditions, but a lack of field-level analyses across climatic, management and soil conditions limits confidence in such predictions. Satellite imagery provides the opportunity to monitor agricultural lands at sub-field resolution across large spatial scales and wide environmental gradients. Here we investigate the maize yield impacts of conservation tillage in the semi-arid western US Corn Belt, using sub-field resolution datasets on tillage practices and crop yields derived from satellite data spanning four states (Nebraska, Kansas, South Dakota, and North Dakota) between 2008 and 2020. On these datasets, we estimate heterogenous yield outcomes for several thousand maize fields across gradients in climate, soil quality and irrigation status by using a causal forests analysis, an adaptation of the random forests machine-learning algorithm for causal inference on observational data. We find that long-term adoption of conservation tillage increased rainfed maize yields by an average of 9.9% in the region. Impacts on irrigated yields were small and not statistically significant. These results, along with an analysis of variables related to greater than average yield benefits, indicate that improved water infiltration and retention are the primary reasons for conservation tillage benefits. Despite yield benefits, many fields estimated to see increased yields under long term low till have not adopted the practice. Therefore, we identify specific counties likely to benefit most from increased levels of adoption. Our results strengthen the understanding of the impacts of conservation agriculture on crop yields and help define environments and counties most likely to benefit from conservation tillage.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Cyber Conservative Operations

In an era of increasingly sophisticated and pervasive cyber threats, robust cyber resilience strategies are more critical than ever. This paper introduces the concept of Cyber Conservative Operations, a proactive approach designed to assist critical infrastructure owners and operators in managing risk and maintaining resilience in the face of imminent, yet not occurring, cyber events. By leveraging the principles of Cyber-Informed Engineering (CIE) and the energy sector’s practice of conservative operations, Cyber Conservative Operations offer a framework for planning and executing coordinated active defense and resilience-oriented actions ahead of cyber events. This approach aims to minimize the consequences of digitally-enabled hazards and ensure swift recovery from anticipated cyber threats. Cyber Conservative Operations enhance the ability of owners and operators to execute pre-planned defense and resilience actions, thereby reducing the impact of digitally-enabled hazards. These operations are crucial for addressing impacts that cannot be precisely quantified or forecasted and for preparing organizations for rapid recovery from imminent digital threats. The paper begins with a discussion of conservative operations as applied to the bulk power system (BPS), a current mechanism allowing BPS entities to enact defensive operating plans to mitigate impending grid unreliability. Building on this model, we present a concept for implementing cyber conservative operations at asset owner facilities. The paper concludes with two case studies of cyber conservative operations drawn from high-profile cyber events, illustrating the practical application and benefits of this proactive approach.

42 - ENGINEERING↗
DOE OSTI2022

Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates

The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating terms containing the covariant component B Ψ P of the magnetic field vector with respect to the poloidal flux function Ψ P . In an unperturbed plasma, B Ψ P can be eliminated via exact coordinate transformations, but, in general, one relies on approximations, assuming that the effect of B Ψ P is small. In this work, we are interested in the question whether Hamiltonian conservation laws are still satisfied when B Ψ P is retained in the presence of fluctuations. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency, and a single toroidal mode number n, we show that simulations using the code ORBIT with and without B Ψ P yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the appendix), which show that the unabridged GC Lagrangian with B Ψ P retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) and (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen) modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A Mass Conservation Relaxed (MCR) LSTM Model for Streamflow Simulation Across CONUS

The recent development of the physics-aware Mass-Conserving Long Short-Term Memory network (MC-LSTM) provides an alternative to other data-driven Deep Learning (DL) models in hydrology. Mass-Conserving Long Short-Term Memory incorporates mass conservation directly into the LSTM architecture. Despite the theoretical advancements, studies have reported a surprisingly limited performance of the MC-LSTM in streamflow simulation. We hypothesize that such a limitation is due to the unrealistic mass conservation scheme in MC-LSTM, which overlooks unobserved incoming water fluxes beyond precipitation. As an attempt to verify this hypothesis, we propose a Mass Conservation Relaxed LSTM (MCR-LSTM), which incorporates a bi-directional mass relaxation (MR) component to account for potential incoming water fluxes beyond precipitation. We train and test the proposed MCR-LSTM model across 531 watersheds in the contiguous United States (CONUS) against three baseline models: the Sacramento Soil Moisture Accounting, LSTM, and MC-LSTM. Our results show that MCR-LSTM outperforms MC-LSTM despite its underperformance compared to LSTM. Specifically, MCR-LSTM's advantage over MC-LSTM is mainly seen in the Plains and Western U.S., where the newly incorporated MR component better simulates water loss and suggests the likely existence of additional incoming water fluxes beyond precipitation, respectively. The novelty and contribution of this study are twofold: firstly, it introduces an alternative physics-aware DL tool (i.e., MCR-LSTM) in hydrology with higher accuracy in specific regions compared to MC-LSTM. Secondly, it provides a diagnosis of regions where strict, precipitation-based mass conservation constraints may be unrealistic in streamflow simulation.

deep learning↗
DOE OSTI2022

Integrating terrestrial scavenging ecology into contemporary wildlife conservation and management

Scavenging plays a vital role in maintaining ecosystem health and contributing to ecological functions; however, research in this sub-discipline of ecology is underutilized in developing and implementing wildlife conservation and management strategies. We provide an examination of the literature and recommend priorities for research where improved understanding of scavenging dynamics can facilitate the development and refinement of applied wildlife conservation and management strategies. Due to the application of scavenging research broadly within ecology, scavenging studies should be implemented for informing management decisions. In particular, a more direct link should be established between scavenging dynamics and applied management programs related to informing pharmaceutical delivery and population control through bait uptake for scavenging species, prevention of unintentional poisoning of nontarget scavenging species, the epidemiological role that scavenging species play in disease dynamics, estimating wildlife mortalities, nutrient transfer facilitated by scavenging activity, and conservation of imperiled facultative scavenging species. This commentary is intended to provide information on the paucity of data in scavenging research and present recommendations for further studies that can inform decisions in wildlife conservation and management. Additionally, we provide a framework for decision making when determining how to apply scavenging ecology research for management practices and policies. Due to the implications that scavenging species have on ecosystem health, and their overall global decline as a result of anthropic activities, it is imperative to advance studies in the field of scavenging ecology that can inform applied conservation and management programs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

An explicit, energy-conserving particle-in-cell scheme

We present an explicit temporal discretization of particle-in-cell schemes for the non-relativistic Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple, second-order explicit scheme that conserves energy exactly in the Eulerian context. We show that direct translation to particle-in-cell does not result in strict conservation, but derive a simple correction based on an analytically solvable optimization problem that recovers conservation. While this optimization problem is not guaranteed to have a real solution for every particle, we provide a correction that makes imaginary values extremely rare and still admits $\mathcal{O}$(10 –12 ) fractional errors in energy for practical simulation parameters. We present the scheme in both electrostatic – where we use the Ampère formulation – and electromagnetic contexts. With an electromagnetic field solve, the field update is most naturally linearly implicit, but the more computationally intensive particle update remains fully explicit. Here, we also show how the scheme can be extended to use the fully explicit leapfrog and pseudospectral analytic time-domain (PSATD) field solvers. The scheme is tested on standard kinetic plasma problems, confirming its conservation properties.

Energy conservation↗
DOE OSTI2022

Quantifying the Impact of Lagged Hydrological Responses on the Effectiveness of Groundwater Conservation

Many irrigated agricultural areas seek to prolong the lifetime of their groundwater resources by reducing pumping. However, it is unclear how lagged responses, such as reduced groundwater recharge caused by more efficient irrigation, may impact the long-term effectiveness of conservation initiatives. Here, we use a variably saturated, simplified surrogate groundwater model to: 1) analyze aquifer responses to pumping reductions, 2) quantify time lags between reductions and groundwater level responses, and 3) identify the physical controls on lagged responses. We explore a range of plausible model parameters for an area of the High Plains Aquifer (USA) where stakeholder-driven conservation has slowed groundwater depletion. We identify two types of lagged responses that reduce the long-term effectiveness of groundwater conservation, recharge-dominated and lateral-flow-dominated, with vertical hydraulic conductivity (K Z ) the major controlling variable. When high K z allows percolation to reach the aquifer, more efficient irrigation reduces groundwater recharge. By contrast, when low K z impedes vertical flow, short term changes in recharge are negligible, but pumping reductions alter the lateral flow between the groundwater conservation area and the surrounding regions (lateral-flow-dominated response). For the modeled area, we found that a pumping reduction of 30% resulted in median usable lifetime extensions of 20 or 25 years, depending on the dominant lagged response mechanism (recharge- vs. lateral-flow-dominated). These estimates are far shorter than estimates that do not account for lagged responses. To conclude, results indicate that conservation-based pumping reductions can extend aquifer lifetimes, but lagged responses can create a sizable difference between the initially perceived and actual long-term effectiveness.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Energy conservation in real-time nuclear–electronic orbital Ehrenfest dynamics

Real-time nuclear–electronic orbital Ehrenfest (RT-NEO-Ehrenfest) dynamics methods provide a first-principles approach for describing nonadiabatic molecular processes with nuclear quantum effects. For an efficient description of proton transfer within RT-NEO-Ehrenfest dynamics, the basis function center associated with the quantum proton can be allowed to move classically. Here, this traveling proton basis (TPB) approach effectively captures proton quantum dynamics, although its energy conservation behavior is not yet fully satisfactory. Two recently proposed TPB approaches, in principle, conserve the extended energy, which includes both the system energy and the kinetic energy associated with the proton basis function center. Herein, a thermostatted TPB approach is proposed to improve the conservation of the system energy, excluding the kinetic energy associated with the proton basis function center. In this approach, the quantum proton dynamics are modulated by dynamically rescaling the proton momentum operator to maintain the system energy conservation. With the excited-state intramolecular proton transfer of o-hydroxybenzaldehyde as an example, this approach is shown to significantly improve the system energy conservation while preserving the accuracy of the quantum proton dynamics as achieved in the original TPB approach.

Ehrenfest dynamics↗