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At least 811 records · Page 45

Multi-Entity Simulation with CoSim Toolbox

Co-simulation is an analysis technique for linking multiple software models during runtime by facilitating data exchange and simulation time synchronization. There are numerous challenges when constructing an effective co-simulation including simulation tool installation, data management, and writing new models in a manner compatible with the co-simulation framework of choice. CoSim Toolbox is an integration of multiple pieces of software designed to make assembling such a co-simulation in HELICS easier. This report summarizes the existing capabilities of CoSim Toolbox and outlines future development plans.

97 MATHEMATICS AND COMPUTING↗

Enclosure fire modeling

A fire characterization methodology is presented, which for the first time provides a unified analysis framework for the integration of all fire tests data on a common basis. Fire temperatures, smoke densities, toxic gas concentrations and heat fluxes to material properties, enclosure geometry, and ventilation factors are provided in this fire characterization approach. The fire characterization methodology was used to develop an enclosure fire hazards analysis procedure capable of predicting the probable course in fire prevention.

Coulbert, C. D.↗

Facilitating Screening of MOFs for Mixed Matrix Membranes Using Machine Learning and the Maxwell Model

Metal organic framework (MOF)-based mixedmatrix membranes (MMMs), which embed MOF particles in polymer matrices, combine the advantages of polymeric and inorganic membranes. Multiple previous studies have used the Maxwell model together with molecular simulations and machine learning (ML) to predict the performance of MOF/polymer MMMs. However, the assumption of rigid MOF frameworks in molecular simulations limited the accuracy of the data used in the predictions, particularly in predicting molecular diffusivities. We developed a novel workflow integrating ML models with consideration of MOF flexibility to predict the permeability and selectivity of 131,722 MMMs for CO 2 /CH 4 , O 2 /N 2 and He/H 2 separations. The full range of achievable MMM performance within the Maxwell model was analyzed, and several promising MOFs were identified using this workflow. This approach offers an efficient tool for screening any polymer and MOF combination in gas separation applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

How good are polarizable and flexible models for water: Insights from a many-body perspective

We present a systematic analysis of state-of-the-art polarizable and flexible water models from a many-body perspective, with a specific focus on their ability to represent the Born–Oppenheimer potential energy surface of water from the gas to the liquid phase. Using coupled cluster data in the completed basis set limit as a reference, we examine the accuracy of the polarizable models in reproducing individual many-body contributions to interaction energies and harmonic frequencies of water clusters and compare their performance with that of MB-pol, an explicit many-body model that has been shown to correctly predict the properties of water across the entire phase diagram. Based on these comparisons, we use MB-pol as a reference to analyze the ability of the polarizable models to reproduce the energy landscape of liquid water under ambient conditions. We find that, while correctly reproducing the energetics of minimum-energy structures, the polarizable models examined in this study suffer from inadequate representations of many-body effects for distorted configurations. To investigate the role played by geometry-dependent representations of 1-body charge distributions in reproducing coupled cluster data for both interaction and many-body energies, we introduce a simplified version of MB-pol that adopts fixed atomic charges and demonstrate that the new model retains the same accuracy as the original MB-pol model. Based on the analyses presented in this study, we believe that future developments of both polarizable and explicit many-body models should continue in parallel and would benefit from synergistic efforts aimed at integrating the best aspects of the two theoretical/computational frameworks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Global Methane Budget 2000-2012

The global methane (CH4) budget is becoming an increasingly important component for managing realistic pathways to mitigate climate change. This relevance, due to a shorter atmospheric lifetime and a stronger warming potential than carbon dioxide, is challenged by the still unexplained changes of atmospheric CH4 over the past decade. Emissions and concentrations of CH4 are continuing to increase, making CH4 the second most important human-induced greenhouse gas after carbon dioxide. Two major difficulties in reducing uncertainties come from the large variety of diffusive CH4 sources that overlap geographically, and from the destruction of CH4 by the very short-lived hydroxyl radical (OH). To address these difficulties, we have established a consortium of multi-disciplinary scientists under the umbrella of the Global Carbon Project to synthesize and stimulate research on the methane cycle, and producing regular (approximately biennial) updates of the global methane budget. This consortium includes atmospheric physicists and chemists, biogeochemists of surface and marine emissions, and socio-economists who study anthropogenic emissions. Following Kirschke et al. (2013), we propose here the first version of a living review paper that integrates results of top-down studies (exploiting atmospheric observations within an atmospheric inverse-modeling framework) and bottom-up models, inventories and data-driven approaches (including process-based models for estimating land surface emissions and atmospheric chemistry, and inventories for anthropogenic emissions, data-driven extrapolations).For the 2003-2012 decade, global methane emissions are estimated by top-down inversions at 558 TgCH4 yr(exp -1), range 540-568. About 60 of global emissions are anthropogenic (range 50-65%). Since 2010, the bottom-up global emission inventories have been closer to methane emissions in the most carbon-intensive Representative Concentrations Pathway (RCP8.5) and higher than all other RCP scenarios. Bottom-up approaches suggest larger global emissions (736 TgCH4 yr(exp -1), range 596-884) mostly because of larger natural emissions from individual sources such as inland waters, natural wetlands and geological sources. Considering the atmospheric constraints on the top-down budget, it is likely that some of the individual emissions reported by the bottom-up approaches are overestimated, leading to too large global emissions. Latitudinal data from top-down emissions indicate a predominance of tropical emissions (approximately 64% of the global budget, less than 30deg N) as compared to mid (approximately 32%, 30-60deg N) and high northern latitudes (approximately 4%, 60-90deg N). Top-down inversions consistently infer lower emissions in China (approximately 58 TgCH4 yr(exp -1), range 51-72, minus14% ) and higher emissions in Africa (86 TgCH4 yr(exp -1), range 73-108, plus 19% ) than bottom-up values used as prior estimates. Overall, uncertainties for anthropogenic emissions appear smaller than those from natural sources, and the uncertainties on source categories appear larger for top-down inversions than for bottom-up inventories and models. The most important source of uncertainty on the methane budget is attributable to emissions from wetland and other inland waters. We show that the wetland extent could contribute 30-40% on the estimated range for wetland emissions. Other priorities for improving the methane budget include the following: (i) the development of process-based models for inland-water emissions, (ii) the intensification of methane observations at local scale (flux measurements) to constrain bottom-up land surface models, and at regional scale (surface networks and satellites) to constrain top-down inversions, (iii) improvements in the estimation of atmospheric loss by OH, and (iv) improvements of the transport models integrated in top-down inversions. The data presented here can be downloaded from the Carbon Dioxide Information Analysis Center (http://doi.org/10.3334/CDIAC/GLOBAL_ METHANE_BUDGET_2016_V1.1) and the Global Carbon Project.

Saunois, Marielle↗

Multiphysics for nuclear energy applications using a cohesive computational framework

With the recent development of advanced numerical algorithms, software design, and low-cost high-performance computer hardware, reliance on coupled multiphysics to predict the behavior of complex physical systems is beginning to become standard practice. This is especially true in nuclear energy applications where strong nonlinear interdependencies exist between reactor physics, radiation transport, multi-scale nuclear fuels performance, thermal fluids, etc. Resolving these nonlinear dependencies requires choices in multiphysics software approaches. Two main multiphysics modeling and simulation approaches have emerged. The first is based upon "code coupling" where disparate physics codes of different software design, code languages, and spatial and temporal integration schemes are coupled together with relatively complex data passing interfaces. The second multiphysics software approach is to employ a "cohesive" framework where all physics applications are developed with a common software design, i.e., data structures, syntax, input format, integrated spatial and temporal discretization schemes, etc. In this paper we present the Multiphysics Object-Oriented Simulation Environment (MOOSE) development and runtime framework and describe the framework's cohesive modeling and simulation multiphysics approach. Then, a "cohesive-like" extension of the MOOSE framework is presented where MOOSE-based physics software applications are efficiently coupled to non-MOOSE (external) physics codes to form multiphysics applications using MOOSE's unique interface capabilities. Finally, several examples of MOOSE's cohesive and cohesive-like multiphysics applications will be demonstrated. These multiphysics demonstrations will incorporate both MOOSE-based applications and external codes, including Nek5000, RELAP-7, TRACE, BISON, and Pronghorn.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Network Anomaly Detection in Distributed Edge Computing Infrastructure

As networks continue to grow in complexity and scale, detecting anomalies has become increasingly challenging, particularly in diverse and geographically dispersed environments. Traditional approaches often struggle with managing the computational burden associated with analyzing large-scale network traffic to identify anomalies. This paper introduces a distributed edge computing framework that integrates federated learning with Apache Spark and Kubernetes to address these challenges. We hypothesize that our approach, which enables collaborative model training across distributed nodes, significantly enhances the detection accuracy of network anomalies across different network types. We show that by leveraging distributed computing and containerization technologies, our framework not only improves scalability and fault tolerance but also achieves superior detection performance compared to state-of-the-art methods. Extensive experiments on the UNSW-NB15 and ROAD datasets validate the effectiveness of our approach, demonstrating statistically significant improvements in detection accuracy and training efficiency over baseline models, as confirmed by MannWhitney U and Kolmogorov-Smirnov tests (p<0.05).

Marfo, William [University of Texas at El Paso,Dep↗

In-Situ Resource Utilization Modeling of a Lunar Water Processing System

A key element of achieving a sustained surface presence, such as defined in NASA’s Artemis plan, is In-Situ Resource Utilization (ISRU). ISRU is the practice of using local resources to provide mission consumables that reduce system launch mass requirements, and regenerate resources (chiefly, water and oxygen) for propulsion and life support supporting both Lunar and Martian missions. ISRU systems require multiple complex processes, such as excavation, chemical reactors, and electrolysis subsystems that must operate in harmony to optimize the overall system process from beginning to end. The Mission Analysis and Integration Tool (MAIT) was previously developed with MATLAB in FY22 to connect individual subsystem models into a customized, flexible framework for the purpose of technology downselect, optimization, and end-to-end process planning. Beginning in FY24, MAIT was leveraged and evolved using MATLAB/Simulink due to its ability to communicate with a vast number of other programming languages and makes up the backbone of data flow between inputs and outputs to the subsystem models. MAIT initially evaluated a suite of ISRU-related technologies, including the water processing Lunar Auger Dryer for ISRU (LADI) system with integrated upstream excavation and downstream electrolysis subsystems. With individual models consolidated, the MAIT tool generated over 60,000 cases during its parametric sweeps; these system iterations produced valuable insight into the optimal LADI geometry for minimizing energy demands, estimating carbothermal reactor and radiator mass relationships, and calculated the power dynamics of the electrolysis unit. Advanced efforts with advanced models will include examining multiple production targets to demonstrate the ability to scale ISRU technologies supporting the Space Technology Mission Directorate’s (STMD) commercialization strategy, and increase the MAIT software capability to handle a wide array of ISRU system models beyond the Lunar environment, e.g. production of propellant for a Martian lander.

Avery Carlson↗

An Extensible Schema-less Database Framework for Managing High-throughput Semi-Structured Documents

Object-Relational database management system is an integrated hybrid cooperative approach to combine the best practices of both the relational model utilizing SQL queries and the object oriented, semantic paradigm for supporting complex data creation. In this paper, a highly scalable, information on demand database framework, called NETMARK is introduced. NETMARK takes advantages of the Oracle 8i object-relational database using physical addresses data types for very efficient keyword searches of records for both context and content. NETMARK was originally developed in early 2000 as a research and development prototype to solve the vast amounts of unstructured and semi-structured documents existing within NASA enterprises. Today, NETMARK is a flexible, high throughput open database framework for managing, storing, and searching unstructured or semi structured arbitrary hierarchal models, XML and HTML.

Maluf, David A.↗

Data for A Hybrid Biophysical-Machine Learning Framework for Diurnal Surface Energy Flux Estimation Using Proximal Sensing

Thermal infrared-based remote sensing of surface energy fluxes has traditionally relied on high spatial resolution satellite data with revisit frequencies on the order of weeks. In this study, we evaluate a biophysics-based analytical surface energy balance model for predicting latent energy (LE) and sensible heat (H) fluxes using proximal sensing observations. The Surface Temperature Initiated Closure (STIC1.2) model has been extensively validated across a wide range of spatial and temporal scales using various satellite-derived thermal infrared data sets. Here we extend this validation by applying STIC at sub-hourly temporal resolution over multiple growing seasons for four distinct agricultural systems. We further develop and evaluate novel STIC variants that incorporate machine learning (ML) techniques to eliminate the need for surface energy balance observations, specifically net radiation and soil heat flux, thereby enhancing model applicability in data-sparse settings. The integration of a ML component to estimate surface available energy is shown to have strong predictive performance for both LE (R2 = 0.81–0.94) and H (R2 = 0.46–0.72) across all agricultural systems examined here, demonstrating the potential of hybrid biophysical-machine learning approaches for surface energy balance modeling with minimal data requirements. This study concludes with a novel application of explainable machine learning (exML) to diagnose sources of model error. This exML framework attributes residual prediction errors to both model input variables and environmental drivers not explicitly included in the simulation experiments. This approach provides a new pathway for improving model design and integrating previously overlooked yet influential variables into future model iterations.

AI/ML↗

An Extensible "SCHEMA-LESS" Database Framework for Managing High-Throughput Semi-Structured Documents

Object-Relational database management system is an integrated hybrid cooperative approach to combine the best practices of both the relational model utilizing SQL queries and the object-oriented, semantic paradigm for supporting complex data creation. In this paper, a highly scalable, information on demand database framework, called NETMARK, is introduced. NETMARK takes advantages of the Oracle 8i object-relational database using physical addresses data types for very efficient keyword search of records spanning across both context and content. NETMARK was originally developed in early 2000 as a research and development prototype to solve the vast amounts of unstructured and semistructured documents existing within NASA enterprises. Today, NETMARK is a flexible, high-throughput open database framework for managing, storing, and searching unstructured or semi-structured arbitrary hierarchal models, such as XML and HTML.

Maluf, David A.↗

The IDAES process modeling framework and model library—Flexibility for process simulation and optimization

Abstract Energy systems and manufacturing processes of the 21st century are becoming increasingly dynamic and interconnected, which require new capabilities to effectively model and optimize their design and operations. Such next generation computational tools must leverage state‐of‐the‐art techniques in optimization and be able to rapidly incorporate new advances. To address these requirements, we have developed the Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform, which builds on the strengths of both process simulators (model libraries) and algebraic modeling languages (advanced solvers). This paper specifically presents the IDAES Core Modeling Framework (IDAES‐CMF), along with a case study demonstrating the application of the framework to solve process optimization problems. Capabilities provided by this framework include a flexible, modifiable, open‐source platform for optimization of process flowsheets utilizing state‐of‐the‐art solvers and solution techniques, fully open and extensible libraries of dynamic unit operations models and thermophysical property models, and integrated support for superstructure‐based conceptual design and optimization under uncertainty.

42 ENGINEERING↗

Particle-hole symmetric slave-boson method for the mixed valence problem

We introduce an analytic slave-boson method for treating the finite-𝑈 Anderson impurity model. Our approach introduces two bosons to track both 𝑄 ⇌ 𝑄 ± 1 valence fluctuations and reduces to a single symmetric 𝑠 boson in the effective action, encoding all the high-energy atomic physics information in the boson's kinematics, while the low-energy part of the action remains unchanged across finite-𝑈, infinite-𝑈, and Kondo limits. We recover the infinite-𝑈- and Kondo-limit actions from our approach and show that the Kondo resonance already develops in the normal state when the slave boson has yet to condense. We show that the slave rotor and 𝑠 boson have the same algebraic structure, and we establish a unified functional integral framework connecting the 𝑠-boson and slave-rotor representations for the single-impurity Anderson model.

Anderson impurity model↗

A Multicomponent Reactive Transport Model for Integrated Surface‐Subsurface Hydrology Problems

Abstract Despite the widespread use of integrated hydrology models in a variety of applications, consideration of multicomponent reactive transport is still not common. The implementation of these processes requires coupling transport at the surface‐subsurface interface and efficient solution of the non‐linear geochemical model that is consistent with the integrated hydrology solution. The Advanced Terrestrial Simulator provides a flexible multiphysics framework that facilitated this process. In this work, the integrated reactive transport process kernel (PK) was weakly coupled to the integrated hydrology PK. In turn, integrated transport and reactions were coupled using an operator splitting approach. This splitting enabled an explicit solution of the integrated transport problem, including a novel algorithm to calculate exchange fluxes across the surface‐subsurface interface and a point‐by‐point solution of the geochemical problem. Geochemical capabilities were added using well‐established external codes, but rather than using a custom interface to each, a generic interface was used that clearly specifies the variables and operations used by the chemistry PK. The implementation is demonstrated with two example simulations: transport of a tracer in a soil column as it saturates over time and water ponds on the surface and reactive transport in a hillslope driven by successive wet‐dry cycles that result in infiltration, runoff and exfiltration processes.

54 ENVIRONMENTAL SCIENCES↗

An ontology to represent synthetic building occupant characteristics and behavior

Since the introduction of the occupant behavior Drivers-Needs-Actions-Systems (DNAS) framework in 2013, researchers have used the framework or further developed it based on their case studies, which include efforts to collect new data on occupant behaviors. The effort is often costly for the relatively few new data points added. Problems emerge when the already collected data do not meet the modelers' interoperability requirements. Previous studies addressed this issue by developing more sophisticated ontologies that enable integration with other datasets and synthetic data methodologies that would meet unique research applications. This paper presents an extension of the DNAS framework for the representation of synthetic occupant data to support various applications and use cases across the building life cycle. An agent-based modeling application is one of our motivations that requires more elaborate characteristics of an occupant-agent or a group-of-agent. The extension, built upon a review of the literature, introduces new elements to the framework that fall into five categories, including socio-economic, geographical location, activities, subjective values, and individual and collective adaptive actions. On-going research includes identifying occupant datasets and developing data fusion methods to generate synthetic occupants, as well as to demonstrate its applications in agent-based modeling coupled with building performance simulation.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Real-Time Health Monitoring for Gas Turbine Components Using Online Learning and High-Dimensional Data

Capital-intensive turbomachinery, such as gas turbines and combined cycle plants, are constantly being monitored for performance anomalies, faults, and physical degradation. Although these power-generating assets are equipped with hundreds of sensors, existing monitoring tools can only handle moderate-sized data. As a result, only a handful of aggregate metrics are used to monitor machine health. At the same time, developing advanced tools suitable for large datasets have been restricted by the lack of appropriate data. The objective of this proposal was to demonstrate a Big Data analytics framework for fault detection and diagnosis in gas turbine applications. We develop a predictive analytics framework methodology guided by these experimental data, industrial data from our collaborators, and physics-based models with engineering domain knowledge. Our analytics framework consists of four key components (1) a data curation process that addresses data storage, data quality assessments, and integrity checks, (2) a feature engineering component that utilizes statistical methods and transformation algorithms guided by physics-based models to extract high-fidelity fault features that can be leveraged for fault detection and classifying fault severities, (3) a Machine Learning-based fault detection and diagnostics algorithms for detecting operational and hardware faults in the combustion and the turbines section. We utilize two industry-class gas turbine component test rigs to generate first of its kind data for critical gas turbine faults with varying severity levels. Advanced gas turbine test facilities will be interrogated using state-of-the-art instrumentation techniques to build fault signatures and data trends for key combustor and turbine faults. Data generated from a combustor test rig (Georgia Tech) and a turbine test rig (Penn State) during both normal operation and with seeded faults serve as the basis for the Big Data sets. The test conditions in the two test facilities include common, critical events that occur in the operation. Utilizing the combustor test rig, we examine two common combustor faults: lean blowout and centerbody degradation. For the turbine section we develop analytic models for monitoring cooling faults in the gas turbine

03 NATURAL GAS↗

Real-Time Health Monitoring for Gas Turbine Components Using Online Learning and High-Dimensional Data (Final Report)

Capital-intensive turbomachinery, such as gas turbines and combined cycle plants, are constantly being monitored for performance anomalies, faults, and physical degradation. Although these power-generating assets are equipped with hundreds of sensors, existing monitoring tools can only handle moderate-sized data. As a result, only a handful of aggregate metrics are used to monitor machine health. At the same time, developing advanced tools suitable for large datasets have been restricted by the lack of appropriate data. The objective of this proposal was to demonstrate a Big Data analytics framework for fault detection and diagnosis in gas turbine applications. We develop a predictive analytics framework methodology guided by these experimental data, industrial data from our collaborators, and physics-based models with engineering domain knowledge. Our analytics framework consists of four key components: (1) a data curation process that addresses data storage, data quality assessments, and integrity checks, (2) a feature engineering component that utilizes statistical methods and transformation algorithms guided by physics-based models to extract high-fidelity fault features that can be leveraged for fault detection and classifying fault severities, (3) a Machine Learning-based fault detection and diagnostics algorithms for detecting operational and hardware faults in the combustion and the turbines section. We utilize two industry-class gas turbine component test rigs to generate first of its kind data for critical gas turbine faults with varying severity levels. Advanced gas turbine test facilities will be interrogated using state-of-the-art instrumentation techniques to build fault signatures and data trends for key combustor and turbine faults. Data generated from a combustor test rig (Georgia Tech) and a turbine test rig (Penn State) during both normal operation and with seeded faults serve as the basis for the Big Data sets. The test conditions in the two test facilities include common, critical events that occur in the operation. Utilizing the combustor test rig, we examine two common combustor faults: lean blowout and centerbody degradation. For the turbine section we develop analytic models for monitoring cooling faults in the gas turbine.

20 FOSSIL-FUELED POWER PLANTS↗

Feeding Ten Billion People Is Possible Within Four Terrestrial Planetary Boundaries

Global agriculture puts heavy pressure on planetary boundaries, posing the challenge to achieve future food security without compromising Earth system resilience. On the basis of process-detailed, spatially explicit representation of four interlinked planetary boundaries (biosphere integrity, land-system change, freshwater use, nitrogen flows) and agricultural systems in an internally consistent model framework, we here show that almost half of current global food production depends on planetary boundary transgressions. Hotspot regions, mainly in Asia, even face simultaneous transgression of multiple underlying local boundaries. If these boundaries were strictly respected, the present food system could provide a balanced diet (2,355 kcal per capita per day) for 3.4 billion people only. However, as we also demonstrate, transformation towards more sustainable production and consumption patterns could support 10.2 billion people within the planetary boundaries analysed. Key prerequisites are spatially redistributed cropland, improved water–nutrient management, food waste reduction and dietary changes. Adoption of the Sustainable Development Goals by all nations in 2015 is the first ever commitment to a world development path that safeguards the stability of the Earth system as a prerequisite for meeting universal human standards1. The longstanding challenge of achieving food security through sustainable agriculture is particularly acute in this context as world agriculture is a leading cause for the current transgressions of multiple planetary boundaries (PBs) globally and regionally2–5. The PB framework is a comprehensive scientific attempt to synoptically define our planet’s biogeophysical limits to anthropogenic interference. It suggests bounds to nine interacting processes that together delineate a Holocene-like Earth system state. The Holocene is chosen as the reference state as it is the only period known to provide a safe operating space for a world population of several billion people, and according to a precautionary principle, the PBs are set in sufficient distance from processes that may critically undermine Earth system resilience and global sustainability. A challenging question, thus, is whether human development goals such as food security can be met while maintaining multiple PBs along with their subglobal manifestations. Further PB transgressions could jeopardize the chances of providing sufficient food for a world population projected to be wealthier and reach >9 billion by 2050. This conundrum portrays a tradeoff between Earth’s biophysical carrying capacity and humankind’s rising food demand, calling in response for radical rethinking of food production and consumption patterns6–9. Yield gap closures, avoidance of excessive input use, shifts towards less resource-demanding diets, food waste reductions and efficient international trade are crucial options for sustainably increasing the food supply10–15. For example, enhancing water-use efficiency on irrigated and rain-fed farms can triple or quadruple crop yields in low-performing systems, suggesting possible global gains of >20% (ref. 16). Even higher gains appear feasible through globally optimized configurations of the land-use pattern17, and cutting food losses by half could generate food for another billion people18. Thus, collective large-scale implementation of such options could sustain food for a further growing world population19. Yet achieving this within a safe operating space as defined by PBs requires not only a halt to but actually a reversal of existing PB transgressions. Previous studies suggest that such a reconciliation might be possible, but these were based on aggregate representations of PBs (not accounting for the spatial patterns of limits, transgressions and interactions) or considered only one boundary in isolation17,20–23. Here, we systematically quantify to what extent current food production depends on local to global transgressions of the PBs for biosphere integrity, land-system change, freshwater use and nitrogen (N) flows, along with the potential of a range of solutions to avoid these transgressions and still increase food supply (Table 1). To this end, we configured an internally consistent process-based model of the terrestrial biosphere including agriculture (LPJmL) with multiple spatially distributed PBs and their interactions. LPJmL is among the longest-established and best-evaluated biosphere models, showing robust performance regarding simulation of, for example, carbon, water and crop yield dynamics (Supplementary Figs. 1 and 2 and Supplementary Table 1; see ref. 24 for a comprehensive benchmarking and Supplementary Methods for more detail on model evaluations). In principle following established definitions4, we refine the computation of some PBs with respect to their regional patterns and interactions (Methods), providing globally gridded precautionary limits to human interference with the Earth system at a level of great detail. In particular, we account for the evidence that many PBs need to be represented spatially explicitly4 to cover their

Gerten, Dieter↗