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DOE OSTI2026

Causality-respecting adaptive refinement for PINNs: enabling precise interface evolution in phase field modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. Here, this study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an ‘overshoot and relocate’ phenomenon in dynamic cases with complex morphologies, showcasing the method’s adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR–causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

Allen-Cahn equations↗

DOE OSTI2020

IC Project: w19_hossfault “Modelling of stick-slip behavior in sheared granular fault gouge & nonlinear elasticity behavior in cracked solid”

Low frequency earthquakes, non-volcanic tremor, and acoustic emissions are examples of weak seismic signals that may help detect major seismic events, i.e., earthquakes. In a laboratory setting, in which stick-slip events are simulated, acoustic emissions are detected far from the stick-slip events. In both, field and laboratory scale cases, the acoustic emission signals are sourced or detected in a volume remote from the volume that spawns the earthquake. Therefore, it is relevant to establish the causal relationship between signals detected on passive, remote monitors and the dynamics of the elastic structures that launch important seismic events. The work conducted under this IC allocation allowed us to utilize a numerical model that let us follow this causality, i.e., examine and connect the dynamics in a granular system (fault gouge), to signals detected on passive remote monitors. It was demonstrated that stress chains are key in the dynamics of granular systems and that their evolution is the source of the acoustic emission.

58 GEOSCIENCES↗

DOE OSTI2021

Linear Response Function Reveals the Most Effective Remote Forcing in Causing September Arctic Sea Ice Melting in CESM

We apply the linear response function method to investigate the most excitable mode of the September Arctic sea ice and its corresponding remote oceanic forcing in climate models. The method is useful in identifying the fundamental, dynamical and causal relationship between the remote forcing and sea ice response. We find that the most excitable mode of the September Arctic sea ice preferentially takes place over the Pacic side of the Arctic and its remote forcing corresponds to a dipole pattern of precipitation anomaly in the tropics with an increase of precipitation over the western and central tropical and subtropical Pacic ocean while a decrease over the Maritime Continent. The tropical precipitation anomaly likely drives a Rossby wave train propagating toward higher latitudes and leads to a ridge anomaly over the Pacic side of the Arctic, resulting in poleward atmospheric heat transport, enhanced downward longwave radiation and thus melting of the sea ice. In addition, a good agreement is found with the leading tropical Arctic teleconnection mode detected in a pre-industrial control simulation, which supports the usefulness and robustness of the linear response function method and the importance of tropical forcing in shaping the sea ice variability.

Wu, Yutian↗

DOE OSTI2019

Causal hydrodynamic fluctuations in non-static and inhomogeneous backgrounds

Highlights: •The fluctuation–dissipation relation is modified by inhomogeneous backgrounds. •The constitutive equations are restricted by causality and fluctuation properties. •The structure of constitutive equation gives a natural cutoff scale of the theory. •The memory function with tensor structures in inhomogeneous backgrounds is obtained. -- Abstract: To integrate hydrodynamic fluctuations, namely thermal fluctuations of hydrodynamics, into dynamical models of high-energy nuclear collisions based on relativistic hydrodynamics, the property of the hydrodynamic fluctuations given by the fluctuation–dissipation relation should be carefully investigated. The fluctuation–dissipation relation for causal dissipative hydrodynamics with the finite relaxation time is naturally given in the integral form of the constitutive equation by the linear-response theory. While, the differential form of the constitutive equation is commonly used in analytic investigations and dynamical calculations for practical reasons. We give the fluctuation–dissipation relation for the general linear-response differential form and discuss the restrictions to the structure of the differential form, which comes from the causality and the positive semi-definiteness of the noise autocorrelation, and also the relation of those restrictions to the cutoff scale of the hydrodynamic fluctuations. We also give the fluctuation–dissipation relation for the integral form in non-static and inhomogeneous background by introducing new tensors, the pathline projectors. We find new modification terms to the fluctuation–dissipation relation for the differential form in non-static and inhomogeneous background which are particularly important in dynamical models to describe rapidly expanding systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Unraveling complex causal processes that affect sustainability requires more integration between empirical and modeling approaches

Scientists seek to understand the causal processes that generate sustainability problems and determine effective solutions. Yet, causal inquiry in nature–society systems is hampered by conceptual and methodological challenges that arise from nature–society interdependencies and the complex dynamics they create. Here, we demonstrate how sustainability scientists can address these challenges and make more robust causal claims through better integration between empirical analyses and process- or agent-based modeling. To illustrate how these different epistemological traditions can be integrated, we present four studies of air pollution regulation, natural resource management, and the spread of COVID-19. The studies show how integration can improve empirical estimates of causal effects, inform future research designs and data collection, enhance understanding of the complex dynamics that underlie observed temporal patterns, and elucidate causal mechanisms and the contexts in which they operate. These advances in causal understanding can help sustainability scientists develop better theories of phenomena where social and ecological processes are dynamically intertwined and prior causal knowledge and data are limited. The improved causal understanding also enhances governance by helping scientists and practitioners choose among potential interventions, decide when and how the timing of an intervention matters, and anticipate unexpected outcomes. Methodological integration, however, requires skills and efforts of all involved to learn how members of the respective other tradition think and analyze nature–society systems.

42 ENGINEERING↗

NASA NTRS1990

Physical consistency in modeling interplanetary magnetohydrodynamic fluctuations

The validity of the Velli, Grappin and Mangeney (1989) model is evaluated. It is argued that the model is incorrect because it mixes different dynamical models, assumes weak nonlinearities, makes predictions that vary with observations, and violates causality. It is proposed that self-similar behavior in the coronal source region of the magnetohydrodynamic fluctuations cause the Kolmogorov-like spectra.

Zhou, Y.↗

DOE OSTI2025

Increasing Mosquito Abundance Under Global Warming

Mosquitoes are a key virus vector that poses significant health threats globally, affecting 700 million individuals and causing 1 million deaths annually. Accurately predicting mosquito abundance and dispersion remains a challenge. Complex interactions between mosquito dynamics and various environmental factors, notably hydrology, contribute to this challenge. Existing models typically focus on precipitation and temperature and often overlook further impacts of hydrological variables within mosquito modeling. In this study, we developed an artificial intelligence‐based model for mosquito dynamics, explicitly accounting for different hydrological variables, such as precipitation, soil moisture and streamflow. Using Toronto, Canada, as a case study, we identified causal relationships between changes in mosquito populations, hydrological factors, vegetation (e.g., leaf area index), and climate variables (e.g., daylight length, precipitation, and temperature). We embedded these relationships into a Long Short‐Term Memory (LSTM) Neural Network Model capable of accurately detecting mosquito dynamics across annual, seasonal, and monthly time scales. The LSTM is able to explain, on average, approximately 40% of the variance in the observed mosquito abundance data. Using the calibrated model, we predicted that the summer season mosquito abundance would increase by ∼16% and ∼19% under an intermediate greenhouse emission scenario, Shared Socioeconomic Pathway (SSP) 2–4.5, and a high greenhouse emission scenario, SSP5‐8.5, respectively. We expect that this model can serve as a valuable tool and inform science‐based decisions affecting mosquito dynamics and public health. It can also build a foundation for future risk analysis at the regional and larger scales.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2009

Diagnosis and Reconfiguration using Bayesian Networks: An Electrical Power System Case Study

Automated diagnosis and reconfiguration are important computational techniques that aim to minimize human intervention in autonomous systems. In this paper, we develop novel techniques and models in the context of diagnosis and reconfiguration reasoning using causal Bayesian networks (BNs). We take as starting point a successful diagnostic approach, using a static BN developed for a real-world electrical power system. We discuss in this paper the extension of this diagnostic approach along two dimensions, namely: (i) from a static BN to a dynamic BN; and (ii) from a diagnostic task to a reconfiguration task. More specifically, we discuss the auto-generation of a dynamic Bayesian network from a static Bayesian network. In addition, we discuss subtle, but important, differences between Bayesian networks when used for diagnosis versus reconfiguration. We discuss a novel reconfiguration agent, which models a system causally, including effects of actions through time, using a dynamic Bayesian network. Though the techniques we discuss are general, we demonstrate them in the context of electrical power systems (EPSs) for aircraft and spacecraft. EPSs are vital subsystems on-board aircraft and spacecraft, and many incidents and accidents of these vehicles have been attributed to EPS failures. We discuss a case study that provides initial but promising results for our approach in the setting of electrical power systems.

Knox, W. Bradley↗

NASA NTRS1997

Dynamical System Analysis of Reynolds Stress Closure Equations

In this paper, we establish the causality between the model coefficients in the standard pressure-strain correlation model and the predicted equilibrium states for homogeneous turbulence. We accomplish this by performing a comprehensive fixed point analysis of the modeled Reynolds stress and dissipation rate equations. The results from this analysis will be very useful for developing improved pressure-strain correlation models to yield observed equilibrium behavior.

Girimaji, Sharath S.↗

DOE OSTI2025

Deep Koopman operators for causal discovery

Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. Thus, applying these methods to study causal dynamics in real-world systems, such as the Earth, is a major challenge. Addressing this shortcoming, we leverage deep learning and a Koopman operator-theoretic formalism to present a class of causal discovery algorithms. Kausal uses deep Koopman operator methods to approximate nonlinear dynamics in a linearized vector space in which traditional causal inference methods such as Granger causality can be more easily applied. Our idealized experiments demonstrate Kausal’s superior ability in discovering and characterizing causal signals compared to existing deep learning and non-deep learning state-of-the-art approaches. Finally, the successful identification of major El Niño and La Niña events in observations showcases Kausal’s skill to handle real-world applications.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Causal Evaluations for Identifying Differences between Observations and Earth System Models

We use a nascent data-driven causal discovery method to find and compare causal relationships in observed data and climate model output. We consider ten different features in the Arctic climate collected from public databases on observational and Energy Exascale Earth System Model (E3SM) data. In identifying and analyzing the resulting causal networks, we make meaningful comparisons between observed and climate model interdependencies. This work demonstrates our ability to apply the PCMCI causal discovery algorithm to Arctic climate data, that there are noticeable similarities between observed and simulated Arctic climate dynamics, and that further work is needed to identify specific areas for improvement to better align models with natural observations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Decision-making based on Markov decision process in integrated artificial reasoning framework—Part I: Theory

This paper presents a decision-making framework based on an integrated artificial reasoning framework and Markov decision process (MDP). The integrated artificial reasoning framework provides a physics-based approach that converts system information into state transition models, and the analysis result will be represented by the transition probabilities that can be used with an MDP to find a traceable and explainable optimal pathway. A dynamic Bayesian network (DBN) is well suited for representing the structure of an MDP. The causality information among process variables (or among subsystems) is mathematically represented in a DBN by the conditional probabilities of the node’s states provided different probabilities of the parent node’s states. To define node states in a physically understandable manner, we used multilevel flow modeling (MFM). An MFM follows the fundamental energy and mass conservation laws and supports the selection of process variables that represent the system of interest so that causal relations among process variables are properly captured. An MFM-based DBN supports developing state transition models in an MDP to capture the effect of process variables of system having physical relations. The operators of the target system can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from component degradation or random failures. We analyzed a simplified exemplary system to illustrate an optimal operational policy using the suggested approach.

Markov decision process↗

DOE OSTI2022

Traversable wormhole dynamics on a quantum processor

The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev–Ye–Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS 2 , and is a new realization of holography. Here, we invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Data for Soil Oxygen Dynamics: A Key Mediator of Tile Drainage Impacts on Coupled Hydrological, Biogeochemical, and Crop Systems

Tile drainage removes excess water and is an essential, widely adopted management practice to enhance crop productivity in the US Midwest and throughout the world. Tile drainage has been shown to significantly change hydrological and biogeochemical cycles by lowering the water table and reducing the residence time of soil water, although examining the complex interactions and feedbacks in an integrated hydrology–biogeochemistry–crop system remains elusive. Oxygen dynamics are critical to unraveling these interactions and have been ignored or oversimplified in existing models. Understanding these impacts is essential, particularly so because tile drainage has been highlighted as an adaptation under projected wetter springs and drier summers in the changing climate in the US Midwest. We used the ecosys model that uniquely incorporates first-principle soil oxygen dynamics and crop oxygen uptake mechanisms to quantify the impacts of tile drainage on hydrological and biogeochemical cycles and crop growth in corn–soybean rotation fields. The model was validated with data from a multi-treatment, multi-year experiment in Washington, IA. The relative root mean square error (rRMSE) for the corn and soybean yield in validation is 5.66 % and 12.57 %, respectively. The Pearson coefficient (r) of the monthly tile flow during the growing season is 0.78. Plant oxygen stress turns out as an emergent property of the equilibrium between the soil oxygen supply and biological demand. The impact of tile drainage on the system is achieved through a series of coupled feedback mechanisms. The model results show that tile drainage reduces the soil water content and enhances soil oxygenation. It additionally increases the subsurface discharge and elevates inorganic nitrogen leaching, with seasonal variations influenced by climate and crop phenology. The improved aerobic condition alleviates crop oxygen stress during wet springs, thereby promoting crop root growth during the early growth stage. The development of greater root density, in turn, mitigates water stress during dry summers, leading to an overall increase in the crop yield by ∼6 %. These functions indicate the potential of tile drainage in bolstering crop resilience to climate change and the use of this modeling tool for large-scale assessments of tile drainage. The model reveals the underlying causal mechanisms that drive the agroecosystem response to drainage on the coupled hydrology, biogeochemistry, and crop system dynamics.

Modeling↗

DOE OSTI2019

High spatiotemporal variability of bacterial diversity over short time scales with unique hydrochemical associations within a shallow aquifer

Understanding microbial community structure and function within the subsurface is critical to assessing overall quality and maintenance of groundwater; however, the factors that determine microbial community assembly, structure, and function in groundwater systems and their impact on water quality remains poorly understood. In this study, three shallow wells (FW301, FW303, FW305) in a non-contaminated shallow aquifer in the ENIGMA-Oak Ridge Field Research Center (Oak Ridge, TN) were sampled approximately 3 times a week over a period of three months to measure changes in groundwater geochemistry and microbial diversity. It was expected that the sampled microbial diversity from two historic field wells (FW301, FW303) would be relatively stable, while diversity from a newer well (FW305) would be less stable over time. The wells displayed some degree of hydrochemical variability over time unique to each well, with FW303 being overall the most stable well and FW301 being the most dynamic based upon dissolved oxygen, conductivity, and nitrate. Community analysis via ss-rRNA paired-end sequencing and distribution-based clustering revealed higher OTU richness, diversity, and variability in groundwater communities of FW301 than the other two wells for diversity binned over all time points. Microbial community composition of a given well was on average > 50% dissimilar to any other well at a given time (days), yet, functional gene diversity as measured with GeoChip remained relatively constant. Similarities in community structure across wells were observed with respect to the presence of 20 shared bacterial groups in all samples in all wells, although at varying levels over the tested time period. Similarity percentage (SIMPER) analysis revealed that variability in FW301 was largely attributed to low abundance, highly-transient populations, while variability in the most hydrochemically stable well (FW303) was due to fluctuations in more highly abundant and frequently present taxa. Additionally, the youngest well FW305 showed a dramatic shift in community composition towards the end of the sampling period that was not observed in the other wells, suggesting possible succession events over time. Time-series analysis using vector auto-regressive models and Granger causality showed unique relationships between richness and geochemistry over time in each well. Finally, these results indicate temporally dynamic microbial communities over short time scales, with day-to-day population shifts in local community structure influenced by available source community diversity and local groundwater hydrochemistry.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Soil oxygen dynamics: a key mediator of tile drainage impacts on coupled hydrological, biogeochemical, and crop systems

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Benchmarking the PCMCI Causal Discovery Algorithm for Spatiotemporal Systems

Causal discovery algorithms construct hypothesized causal graphs that depict causal dependencies among variables in observational data. While powerful, the accuracy of these algorithms is highly sensitive to the underlying dynamics of the system in ways that have not been fully characterized in the literature. In this report, we benchmark the PCMCI causal discovery algorithm in its application to gridded spatiotemporal systems. Effectively computing grid-level causal graphs on large grids will enable analysis of the causal impacts of transient and mobile spatial phenomena in large systems, such as the Earth’s climate. We evaluate the performance of PCMCI with a set of structural causal models, using simulated spatial vector autoregressive processes in one- and two-dimensions. We develop computational and analytical tools for characterizing these processes and their associated causal graphs. Our findings suggest that direct application of PCMCI is not suitable for the analysis of dynamical spatiotemporal gridded systems, such as climatological data, without significant preprocessing and downscaling of the data. PCMCI requires unrealistic sample sizes to achieve acceptable performance on even modestly sized problems and suffers from a notable curse of dimensionality. This work suggests that, even under generous structural assumptions, significant additional algorithmic improvements are needed before causal discovery algorithms can be reliably applied to grid-level outputs of earth system models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Delayed coastal inundations caused by ocean dynamics post-Hurricane Matthew

Post Hurricane Abnormal Water Level (PHAWL) poses a persistent inundation threat to coastal communities, yet unresolved knowledge gaps exist regarding its spatiotemporal impacts and causal mechanisms. Using a high-resolution coastal model with a set of observations, we find that the PHAWLs are up to 50 cm higher than the normal water levels for several weeks and cause delayed inundations around residential areas of the U.S. Southeast Coast (USSC). Numerical experiments reveal that while atmospheric forcing modulates the coastal PHAWLs, ocean dynamics primarily driven by the Gulf Stream control the mean component and duration of the shelf-scale PHAWLs. Because of the large spatial impact of the post-hurricane oceanic forcing, the coastal hazards are not limited to a direct hit from a hurricane but can be detected throughout the USSC where the oceanic processes reach.

54 ENVIRONMENTAL SCIENCES↗