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At least 307 records · Page 17

Kilonova light-curve interpolation with neural networks

Kilonovae are the electromagnetic transients created by the radioactive decay of freshly synthesized elements in the environment surrounding a neutron star merger. To study the fundamental physics in these complex environments, kilonova modeling requires, in part, the use of radiative transfer simulations. The microphysics involved in these simulations results in high computational cost, prompting the use of emulators for parameter inference applications. Utilizing a training set of 22 248 high-fidelity simulations (composed of 412 unique ejecta parameter combinations evaluated at 54 viewing angles), we use a neural network to efficiently train on existing radiative transfer simulations and predict light curves for new parameters in a fast and computationally efficient manner. Our neural network can generate millions of new light curves in under a minute. We discuss our emulator's degree of off-sample reliability and parameter inference of the AT2017gfo observational data. Finally, we discuss tension introduced by multiband inference in the parameter inference results, particularly with regard to the neural network's recovery of viewing angle. Published by the American Physical Society 2024

79 ASTRONOMY AND ASTROPHYSICS↗

Surrogate models for linear response

Linear response theory is a well-established method in physics and chemistry for exploring excitations of many-body systems. In particular, the quasiparticle random-phase approximation (QRPA) provides a powerful microscopic framework by building excitations on top of the mean-field vacuum; however, its high computational cost limits model calibration and uncertainty quantification studies. Here, we present two complementary QRPA surrogate models and apply them to study response functions of finite nuclei. One is a reduced-order model that exploits the underlying QRPA structure, while the other utilizes the recently developed parametric matrix model algorithm to construct a map between the system’s Hamiltonian and observables. Our benchmark applications, the calculation of the electric dipole polarizability of 180 Yb and the 𝛽-decay half-life of 80 Ni, show that both emulators can achieve 0.1%–1% accuracy while offering a 6–7 orders of magnitude speedup compared to state-of-the-art QRPA solvers. These results demonstrate that the developed QRPA emulators are well positioned to enable Bayesian calibration and large-scale studies of computationally expensive physics models describing the properties of many-body systems.

Beta decay↗

Data-driven Modeling for Grid Edge IBRs: A Digital Twin Perspective of User-Defined Models

Recent events in Odessa have brought attention to the challenges associated with the interaction between Inverter- Based Resources (IBRs) and the transmission and distribution system. The NERC event diagnosis report has highlighted sev- eral issues, emphasizing the need for continuous performance monitoring of these IBRs by system operators. Key areas of concern include the mismatch of control and protection perfor- mance of IBRs between the original equipment manufacturer (OEM)-provided models and field measurements. The inability to replicate the realistic response can result in incorrect reliability and resilience studies. In this paper, we developed an approach on how to emulate the behavior of an IBR using measurement data obtained for system operators to utilize in real-time and long- term planning. Two experiments are conducted in the phasor domain and electromagnetic transients (EMT) domain to emulate the behavior for grid forming and grid following inverters under various operating conditions and the effectiveness of the proposed model is demonstrated in terms of accuracy and ease of utilizing user-defined models (UDMs)

Mahapatra, Kaveri [BATTELLE (PACIFIC NW LAB)]↗

Design, Modeling, and Control of a Hardware-in-the-Loop Testbed for Off-Road Vehicles

This paper presents the design, modeling, and control of a hardware-in-the-loop (HIL) testbed for off-road vehicles. The proposed HIL testbed employs a transient hydrostatic dynamometer to load a diesel engine to emulate any loading cycles of a wheel loader, which is a representative off-road vehicle. A fully validated wheel loader model is used to calculate the engine load, including both the drive and work functions. Besides, iterative learning control (ILC) has been designed for the loading torque tracking of the hydrostatic dynamometer to ensure accurate emulation of real-world operation scenarios. The developed HIL testbed is used to demonstrate more than 26% energy benefits of automated wheel loaders through systematic optimization compared with human-operated wheel loaders. As a result, this HIL testbed serves as a robust platform for advancing research and development across various off-road vehicles, including excavators, tractors, and harvesters.

33 ADVANCED PROPULSION SYSTEMS↗

DEVELOPMENT AND DEMONSTRATION TESTBED FOR THE REMOTE OPERATIONS AND MONITORING OF MICROREACTORS

The nuclear industry is rapidly developing many advanced-reactor concepts for near-term deployment in both traditional and non-traditional nuclear-powered applications. One such category of advanced reactor is the microreactor, a class of reactor with less than 20MWth power output, intended for applications where the economics or logistics of traditional power sources are difficult. This includes applications such as remote communities, mining sites, defense installations, or humanitarian and disaster-relief missions. One key enabling feature for the successful deployment of microreactors is a remote operations capability. Remote operations provide monitoring and control capabilities which can significantly reduce staffing costs by eliminating the need for licensed operators at each reactor facility and improve the economic viability for microreactor deployment. A remote concept of operations is not currently an established capability in the nuclear industry. In addition, no demonstration microreactor is expected to complete construction or go critical until at least 2026. This leaves two major capability gaps: the successful demonstration of a remote concept of operations for microreactors and a test bed suitable for said demonstration. Both gaps must be addressed in order to advance the remote concepts of nuclear operation and, more broadly, microreactors themselves from paper to reality. This paper aims to fill these gaps and describes a test bed that would support development and deployment of a remote concept of nuclear operations, initial experimental results from that test bed, and the application of the test bed and experimental results for a digital-twin-based remote concept of operations underdevelopment at Idaho National Laboratory (INL). The platform chosen as a remote concept of nuclear operations test bed is the Single Primary Heat Extraction and Removal Emulator, known as SPHERE, located at INL. SPHERE is a small-scale non-nuclear test bed that emulates thermal behavior of a microreactor. The small-scale and non-nuclear nature of SHPERE limit safety concerns associated with remote operations while still providing the physical response representative of a microreactor. A network connection was added to SPHERE that enables remote-monitoring capability. This allows for real-time data streaming to networked workstations, data historians, and human-machine interfaces (HMIs). These are all critical components in a remote concept of operations, thus providing a robust development and demonstration platform. An initial experiment was performed using the SPHERE remote operations testbed. This included running a comprehensively instrumented SPHERE through a series of steady-state and transient operating scenarios in both normal and abnormal operating conditions, all while streaming live test data to a remote HMI and data warehouse. This initial experiment served three purposes: (1) characterizing the response of SPHERE, (2) demonstrating the remote connection to SPHERE, and (3) providing a baseline data set for development of a digital-twin-based remote concept of operations that is under development at INL.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Elastic Bayesian Model Calibration

Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have resulted in tools for emulation, sensitivity analysis, and calibration that are widely used. However, many of these tools do not perform well when the computer model’s parameters control both the amplitude variation of the functional output and its alignment (or phase variation). This paper introduces a framework for Bayesian model calibration when the model responses are misaligned functional data. The approach generates two types of data out of the misaligned functional responses: (1) aligned functions so that the amplitude variation is isolated and (2) warping functions that isolate the phase variation. These two types of data are created for the computer simulation data (both of which may be emulated) and the experimental data. The calibration approach uses both types so that it seeks to match both the amplitude and phase of the experimental data. The framework is careful to respect constraints that arise, especially when modeling phase variation, and is framed in a way that it can be done with readily available calibration software. In conclusion, we demonstrate the techniques on two simulated data examples and on two dynamic material science problems: a strength model calibration using flyer plate experiments and an equation of state model calibration using experiments performed on the Sandia National Laboratories’ Z-machine.

97 MATHEMATICS AND COMPUTING↗

ISO_Fortran_binding_m v0.1.0

The Fortran programming language standard defines a broad feature set supporting the interoperability of Fortran programs with program written according to the C programming language standard. Among Fortran's C-interoperability features is a a C header file "ISO_Fortran_binding.h" This header file defines the interface to various C data structures and functions that C programs may use to access Fortran data entities. The ISO_Fortran_binding_m software defines a native Fortran module that presents an interface to these same data structures and functions. ISO_Fortran_bind_m thus enables Fortran programs to access and manipulate Fortran entities in ways that precisely mirror what C programs can do using ISO_Fortran_binding.h. ISO_Fortran_binding_m facilitates writing portable standard-conforming Fortran programs that emulate non-interoperable features, e.g., dynamic polymorphism, in a standard-conforming interoperable way similar but broader than what is demonstrated in Berkeley Lab's Caffeine software [1]. ISO_Fortran_binding_m also enables a Fortran programmer to extend Fortran's capabilities to emulate certain C functionality such as memory address arithmetic or computing C's "sizeof" function. [1] https://github.com/BerkeleyLab/caffeine/blob/213e3df1c319f0663306354414f352acda42a24f/src/caffeine/collective_subroutines/co_reduce_s.f90#L88 [2] https://github.com/BerkeleyLab/ISO_Fortran_binding_m/blob/0c585362bb4f2c72cf9049c800a7115b529ec533/src/iso_fortran_binding_m.F90#L196

Rouson, Damian↗

Calibration and Rapid-Adoption Forecasting Techniques

CRAFT (Calibration and Rapid-Adoption Forecasting Techniques) CRAFT is a Python-based project for processing, analyzing, and modeling atmospheric or environmental data. It uses machine learning techniques, specifically Random Forest Regression, to create emulators for various environmental variables such as gross primary production and soil water content. It then uses these emulators to robustly test the parameter space of mechanistic models to provide posterior estimations of the free parameters.

Robins, Zachary↗

Machine Learned Empirical Numerical Integrator from Simulated Data

Recently, a number of state-of-the-art surrogate machine learning (ML) models have been designed for global weather and climate prediction, which have been trained using reanalysis data products. Reanalysis data products are constructed using numerical model simulations that combine numerical integration of partial differential equations and parameterization schemes. These products are typically only archived and made available using coarsened spatial and temporal resolutions. This study explores the impact of the numerical generation methods used to produce the training datasets and the temporal resolution of those datasets on machine learning surrogate models. Using the nonlinear vector autoregression (NVAR) machine as an explainable ML technique, simple dynamical systems are emulated with ML models trained on data produced by three classical numerical integration schemes. NVAR is validated as a skillful ML method, capable of producing accurate predictions and, more importantly, reconstructing both the underlying dynamics and the numerical integration scheme used to generate the training data. However, the machine fails to generalize predictions on unseen test data generated by different numerical integration schemes, despite the underlying dynamical system being the same. This result provides a word of caution for the growing field of machine learning emulation of weather and climate dynamics. Furthermore, we illustrate using NVAR that training on temporally coarsened data may increase the required complexity of ML models and potentially introduce new numerical challenges. Finally, we discover that empirical integration schemes with arbitrary time-stepping sizes can be constructed directly from the data, which implies a potential for the development of empirical numerical integration schemes.

54 ENVIRONMENTAL SCIENCES↗

Extratropical Cloud Feedback Constrained by Cloud Sources and Sinks in Cyclones

Constraining cloud feedback in global climate models (GCMs) using observations is important for establishing accurate predictions of future climate. Uncertainty in shortwave cloud feedback (SW FB ) dominates uncertainty in total cloud feedback. Recent studies show a shift toward more positive extratropical SW FB in the latest generations of GCMs leading to the emergence of very high equilibrium climate sensitivity (ECS). In this study, we use precipitation efficiency and albedo susceptibility to constrain liquid water path (LWP) response to warming and SW FB in the Southern Ocean (SO; 50°–80°S). We analyze precipitation in extratropical cyclones (ECs) to learn about extratropical condensed water sink processes, combined with observations of clouds and moisture convergence, and use the analysis to better understand and constrain SW FB . We utilize a perturbed parameter ensemble (PPE) hosted in the Community Atmosphere Model, version 6 (CAM6), to provide a constraint on SW FB based on observations from Clouds and the Earth’s Radiant Energy System (CERES) and Multisensor Advanced Climatology of LWP (MAC-LWP). We apply Gaussian process regression to emulate the model response to all parameters perturbed in the PPE. Confronting the emulator output with observations provides a new estimated response of Earth to global warming. Furthermore, our new estimates of SO LWP reduce the PPE range by 66%–72%, which results in a shortwave cloud radiative effect estimated range that is 27%–34% less than the PPE range. Observations suggest a more positive SO SW FB than the Community Earth System Model, version 2 (CESM2), and consequently do not reject the high climate sensitivity GCMs emerging from the Coupled Model Intercomparison Project phase 6 (CMIP6).

Atmosphere↗

Data for The Value of Reversible Carbon Storage in a Zero-Emissions World

Atmospheric carbon dioxide removal (CDR) is required to stabilize global temperature. CDR can be achieved via ecosystem-based approaches that are cost-effective but reversible (e.g., soil and forest management) or by more durable but expensive approaches (e.g., direct air capture coupled with geologic storage). Here, we examine trade-offs between these approaches, focusing on timing, climate impacts, and cost. We simulated reversible carbon accrual for a range of CDR contract structures using a general minimalist model of ecosystem carbon cycling, and parameterized it to simulate US agricultural soil management─specifically cover cropping─as a case study. We then quantified the resulting impact on atmospheric carbon and global temperature using a climate model emulator. We find that maintaining a patchwork of reversible CDR projects by replacing lapsed projects with new projects can reduce warming by 22–195 μ°C in 2100 and that the magnitude of this cooling effect depends on how effectively the patchwork is maintained. Long-term maintenance of reversible CDR projects requires institutional stability that cannot be guaranteed over multiple decades. Consequently, effective CDR ultimately requires replacing reversible projects with durable projects. To address this problem, we modeled the cost of replacing reversible agricultural soil CDR with geologic CDR. We found that using reversible CDR as a bridge to durable CDR is potentially more cost-effective as a global cooling strategy (0.20–0.81 billion USD per μ°C avoided) than perpetual maintenance of reversible CDR (0.32–1.31 billion USD per μ°C avoided) or an immediate transition to durable CDR (1.37–2.19 billion USD per μ°C avoided). However, we emphasize that institutional commitments to maintain reversible CDR projects cannot be guaranteed. Reliance on reversible CDR as a bridge to durable CDR therefore carries an unknown amount of risk and will only function if efforts to maintain reversible CDR are robust.

Carbon↗

EVSE Characterization

NextGen Profiles' EVSE characterization efforts explored performance variability in production EVSE through the use of EV emulation equipment and assessed how different operational conditions influence charging behavior. Data were collected at a frequency of 10 Hz from both the EV emulator and EVSE during each charge session and stored in a time-series database for further analysis. As part of the NextGen Profiles project, characterization of high-power EVSE was performed on both conductive and wireless charging infrastructure; however, only conductive charging data are currently included in this repository. This EVSE characterization was performed over a range of DC output currents and voltages, covering both nominal and off-nominal test conditions. This EVSE characterization dataset includes high-power charging data from two types of 350-kW-capable EVSE using liquid-cooled Combined Charging System-1 (CCS1, North American version) cables and connectors. To protect confidentiality, all EVSE metadata are anonymized, and the publicly released datasets are metered at 10-Hz frequency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Vulcan Test Platform: Demonstrating the Data Center as a Flexible Grid Asset

Explosive data center demand is outpacing grid infrastructure development. AI workloads and hyperscale cloud growth are creating unprecedented power requirements, while traditional grid expansion faces multi-year development timelines, regulatory hurdles, and decarbonization challenges. Sidewalk Infrastructure Partners recognized this impending crisis years ago and founded Verrus to develop an innovative solution: data centers that function as grid assets rather than passive loads. The Verrus approach integrates proprietary grid-aware controls with battery energy storage systems (BESS) in a medium-voltage architecture that delivers three critical capabilities: Fast-responding demand flexibility that can service requests from the utility within 10 seconds, Uninterrupted transition to islanded operation during grid disturbances, Continuous uptime assurance while maintaining all customer service level commitments Through Verrus' strategic partnership with the National Renewable Energy Laboratory (NREL), we validated these capabilities on Vulcan, a 70 MW utility-scale test platform powered by NREL's ARIES Virtual Emulation Environment. This deployment-ready technology has successfully demonstrated that Verrus data centers can deliver meaningful grid services while maintaining mission-critical reliability. This technical report outlines the design, methodology, and results of this emulated deployment, demonstrating that data centers can play a pivotal role in enhancing grid flexibility and reliability, without sacrificing service level guarantees.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Practical Insights on Applying Simulation-Based Control Methods in Experimental Studies

Advanced nuclear reactors are crucial to the future of energy both in the United States and around the globe. In contrast to the current operating fleet, they are characterized as being deployable in remote locations and able to operate in semi-autonomous or autonomous fashion. This leap forward necessitates a new reactor control paradigm. Because advanced nuclear reactors are still under development in the United States, the creation of new control methods to achieve autonomous operations has been based on systems modeling and simulation. However, an important factor in successfully deploying these new control methods is the ability to seamlessly transition from simulation environments to real-world settings. Control methods tested in both simulation and experimental settings need to be investigated in the context of advanced reactor applications. This work developed a series of simple controllers for Idaho National Laboratory (INL)’s Microreactor Applications Research Validation and Evaluation (MARVEL) microreactor operating in load-following scenarios. These controllers were tested in both simulation and experimental settings, and a comparative performance analysis was performed. The simulation tests leveraged the Control and Optimization Modular Modeling Application for Nuclear Deployment (COMMAND) software developed in a previous stage of the current effort, along with the MARVEL Reactor Excursion and Leak Analysis Program (RELAP5-3D) and Monte Carlo N-Particle (MCNP) models. The experimental tests leveraged the COMMAND software, MARVEL models, and the U.S. Department of Energy Microreactor Program’s Microreactor Automated Control System (MACS). MACS was developed to serve as a control method testbed. It was customized to mirror the MARVEL microreactor, and COMMAND enabled MACS to emulate the physics of MARVEL. The load-following controller was developed using the simulation platform, with efforts to emulate real systems by introducing actuator saturation and noise. These factors were incrementally accounted for in the controller design. After finalizing the controller design, it was implemented with the experimental setup. The experimental conditions tested included an initial test under conditions similar to the final simulation test, and two additional scenarios. The first scenario introduced additional actuator saturation to account for equipment aging over time, which was unknown to the controller. The second scenario introduced sensor delay, a phenomenon anticipated with the use of remote operations or wireless communication in advanced reactors. These tests revealed several notable differences. While the controller performed well in simulation, it exhibited several limitations when transitioning to hardware. The main challenges involved maintaining the steady-state target power, as evidenced by larger error values between the true reactor power and setpoint power, as well as persistent oscillations in controlled reactor power. These issues could lead to unacceptable transient conditions in real reactor testing. Introducing actuator aging and stochastic delays in the experimental setup significantly impacted controller performance, resulting in increased overshoot and undershoot, and exacerbated error and oscillations previously mentioned. These findings underscore the importance of experimental testbeds for testing and validating control methods, as controllers developed using only theory and/or simulation may perform unexpectedly when applied to actual hardware. This research emphasizes the need for an experimental testbed for achieving such validation.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

Joint Analysis of Small-scale Galaxy Clustering and Galaxy–Galaxy Lensing from BOSS Galaxies

We present a joint analysis of galaxy clustering and galaxy–galaxy lensing measurements from BOSS galaxies using a simulation-based emulation method combined with a halo occupation distribution model. Our emulators are constructed with the Aemulus ν simulations, a suite of wνCDM N-body simulations with massive neutrinos as independent particle species. We combine small-scale analysis of clustering from 0.1 to 60.2 h −1 Mpc and lensing from 1.7 to 60.2 h −1 Mpc to perform cosmological constraints. We split the BOSS galaxies into three redshift bins to measure their clustering and employ galaxies from Dark Energy Camera Legacy Survey and Hyper Suprime-Cam as source galaxies to measure lensing separately. We find that the addition of lensing significantly improves the constraining power on $S_8 = σ_8(Ω_m/0.3)^{0.5}$, with a weak improvement for fσ 8 . Our results of fσ 8 indicate tensions of around 1σ−4σ below the results of the cosmic microwave background observations of Planck. For S 8 , our results are also lower than Planck, and the tension can be mitigated when considering possible systematics in lensing measurement. As a by-product, our analysis prefers a nonzero neutrino mass but without strong significance, with the constraining power dominated by the clustering. Given the accuracy and precision of our model and the observational data, it is anticipated that larger and higher-quality spectroscopic data sets will improve the constraints on this fundamental property in the near future.

Gao, Wenhao [Shanghai Jiao Tong University (China)↗

Characterization of DESI fiber assignment incompleteness effect on 2-point clustering and mitigation methods for DR1 analysis

We present an in-depth analysis of the fiber assignment incompleteness in the Dark EnergySpectroscopic Instrument (DESI) Data Release 1 (DR1). This incompleteness is caused by therestricted mobility of the robotic fiber positioner in the DESI focal plane, which limits thenumber of galaxies that can be observed at the same time, especially at small angular separations.As a result, the observed clustering amplitude is suppressed in a scale-dependent manner, which,if not addressed, can severely impact the inference of cosmological parameters. We discuss themethods adopted for simulating fiber assignment on mocks and data. In particular, we introducethe fast fiber assignment (FFA) emulator, which was employed to obtain the power spectrumcovariance adopted for the DR1 full-shape analysis. We present the mitigation techniques,organised in two classes: measurement stage and model stage. We then use high fidelity mocks as areference to quantify both the accuracy of the FFA emulator and the effectiveness of the differentmeasurement-stage mitigation techniques. This complements the studies conducted in a parallelpaper for the model-stage techniques, namely the θ-cut approach. We find that pairwiseinverse probability (PIP) weights with angular upweighting recover the “true” clustering in allthe cases considered, in both Fourier and configuration space. Notably, we present the first everpower spectrum measurement with PIP weights from real data.

79 ASTRONOMY AND ASTROPHYSICS↗

Uncertainty-informed selection of CMIP6 Earth System Model subsets for use in multisectoral and impact models

Earth system models (ESMs) and general circulation models (GCMs) are heavily used to provide inputs to sectoral impact and multisector dynamic models, which include representations of energy, water, land, economics, and their interactions. Therefore, representing the full range of model uncertainty, scenario uncertainty, and interannual variability that ensembles of these models capture is critical to the exploration of the future co-evolution of the integrated human–Earth system. The pre-eminent source of these ensembles has been the Coupled Model Intercomparison Project (CMIP). With more modeling centers participating in each new CMIP phase, the size of the model archive is rapidly increasing, which can be intractable for impact modelers to effectively utilize due to computational constraints and the challenges of analyzing large datasets. In this work, we present a method to select a subset of the latest phase, CMIP6, featuring models for use as inputs to a sectoral impact or multisector dynamics models, while prioritizing preservation of the range of model uncertainty, scenario uncertainty, and interannual variability in the full CMIP6 ensemble results. This method is intended to help impact modelers select climate information from the CMIP archive efficiently for use in downstream models that require global coverage of climate information. This is particularly critical for large-ensemble experiments of multisector dynamic models that may be varying additional features beyond climate inputs in a factorial design, thus putting constraints on the number of climate simulations that can be used. We focus on temperature and precipitation outputs of CMIP6 models, as these are two of the most used variables among impact models, and many other key input variables for impacts are at least correlated with one or both of temperature and precipitation (e.g., relative humidity). Besides preserving the multi-model ensemble variance characteristics, we prioritize selecting CMIP6 models in the subset that preserve the very likely distribution of equilibrium climate sensitivity values as assessed by the latest Intergovernmental Panel on Climate Change (IPCC) report. This approach could be applied to other output variables of climate models and, possibly when combined with emulators, offers a flexible framework for designing more efficient experiments on human-relevant climate impacts. It can also provide greater insight into the properties of existing CMIP6 models.

Snyder, Abigail C.↗

QuadTune version 1: a regional tuner for global atmospheric models

When a new, better-formulated physical parameterization is introduced into a global atmospheric model, aspects of the global model solutions are sometimes degraded. Then, in order to use the new global model to address science questions, there is an incentive to restore its accuracy. Oftentimes this restoration is achieved by tuning of model parameter values. Unfortunately, the retuning process is expensive because characterizing the parameter dependence requires numerous time-consuming global simulations. To reduce the cost of tuning, this manuscript introduces a “poor man's” model tuner, “QuadTune”. QuadTune carves the globe into regions and approximates the model parameter dependence through the use of an uncorrelated quadratic emulator (i.e., response surface). The simplicity of the emulator reduces the required number of global model simulations and aids explainability of tuner behavior. Tuning removes parametric error but leaves behind model structural error. Structural error manifests itself as regional residual biases, such as stubborn biases and tuning trade-offs. To visualize these residual biases, QuadTune's software includes a set of diagnostic plots. This paper illustrates the use of the plots for characterizing residual biases with an example tuning problem.

Environmental sciences↗