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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Stochastic Adaptive Droop Control in Frequency Regulation of Power Systems With Intermittent Generators

Modern power systems (MPSs), including microgrids (MGs), are increasingly incorporating multiple renewable energy sources (RESs) such as wind and solar power, as well as battery storage and controllable loads. While environmentally beneficial, these sources pose challenges for control and management due to their intermittent and stochastic nature, especially in maintaining frequency stability with multiple interconnected generators of varying capacities. Traditional droop control methods are effective in systems with generators that are dispatchable and have fixed generation capacities, but they fall short when applied to systems with RESs, where generation capacities are dynamic and affected by unpredictable environmental conditions. To address these challenges, this paper introduces a novel stochastic adaptive droop control (SADC) method for load frequency control (LFC). The proposed method adapts droop coefficients in real time, based on the measured stochastic data of power generation capacities, enabling more effective frequency regulation in systems with variable and intermittent power generation. Unlike traditional adaptive control methods, which assume constant or slowly-varying system parameters, this approach accounts for stochastic processes by modeling them as Markov chains, enabling robust performance under highly dynamic and unpredictable conditions. The key contributions of this work include the development of real-time droop coefficient adaptation algorithms, derivation of their stability and convergence properties, and the demonstration of the advantages of the method through simulations. Case studies highlight the improved performance of frequency regulation, particularly in addressing the impact of stochastic weather conditions and the benefits of reducing dependence on battery reserves in dealing with intermittency of RESs. Finally, this paper provides a comprehensive analysis of the theoretical foundations of the method, as well as practical implementation insights for future power systems with high penetration of RESs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market

In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.

Bilevel multistage stochastic programming problem↗
NASA NTRS1978

Stochastic partial differential equations in turbulence related problems

The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.

Chow, P.-L.↗
NASA NTRS1999

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Williams Colin P.↗
NASA NTRS2010

Vestibular Stochastic Resonance as a Method to Improve Balance Function: Optimization of Stimulus Characteristics

Stochastic resonance (SR) is a mechanism by which noise can assist and enhance the response of neural systems to relevant sensory signals. Application of imperceptible SR noise coupled with sensory input through the proprioceptive, visual, or vestibular sensory systems has been shown to improve motor function. Specifically, studies have shown that that vestibular electrical stimulation by imperceptible stochastic noise, when applied to normal young and elderly subjects, significantly improved their ocular stabilization reflexes in response to whole-body tilt as well as balance performance during postural disturbances. The goal of this study was to optimize the characteristics of the stochastic vestibular signals for balance performance during standing on an unstable surface. Subjects performed a standardized balance task of standing on a block of 10 cm thick medium density foam with their eyes closed for a total of 40 seconds. Stochastic electrical stimulation was applied to the vestibular system through electrodes placed over the mastoid process behind the ears during the last 20 seconds of the test period. A custom built constant current stimulator with subject isolation delivered the stimulus. Stimulation signals were generated with frequencies in the bandwidth of 1-2 Hz and 0.01-30 Hz. Amplitude of the signals were varied in the range of 0- +/-700 micro amperes with the RMS of the signal increased by 30 micro amperes for each 100 micro amperes increase in the current range. Balance performance was measured using a force plate under the foam block and inertial motion sensors placed on the torso and head segments. Preliminary results indicate that balance performance is improved in the range of 10-25% compared to no stimulation conditions. Subjects improved their performance consistently across the blocks of stimulation. Further the signal amplitude at which the performance was maximized was different in the two frequency ranges. Optimization of the frequency and amplitude of the signal characteristics of the stochastic noise signals on maximizing balance performance will have a significant impact in its development as a unique system to aid recovery of function in astronauts after long duration space flight or for people with balance disorders.

Mulavara, Ajitkumar↗
NASA NTRS2010

Stimulus Characteristics for Vestibular Stochastic Resonance to Improve Balance Function

Stochastic resonance (SR) is a mechanism by which noise can enhance the response of neural systems to relevant sensory signals. Studies have shown that imperceptible stochastic vestibular electrical stimulation, when applied to normal young and elderly subjects, significantly improved their ocular stabilization reflexes in response to whole-body tilt as well as balance performance during postural disturbances. The goal of this study was to optimize the amplitude characteristics of the stochastic vestibular signals for balance performance during standing on an unstable surface. Subjects performed a standard balance task of standing on a block of foam with their eyes closed. Bipolar stochastic electrical stimulation was applied to the vestibular system using constant current stimulation through electrodes placed over the mastoid process behind the ears. Amplitude of the signals varied in the range of 0-700 microamperes. Balance performance was measured using a force plate under the foam block, and inertial motion sensors were placed on the torso and head. Balance performance with stimulation was significantly greater (10%-25%) than with no stimulation. The signal amplitude at which performance was maximized was in the range of 100-300 microamperes. Optimization of the amplitude of the stochastic signals for maximizing balance performance will have a significant impact on development of vestibular SR as a unique system to aid recovery of function in astronauts after long-duration space flight or in patients with balance disorders.

Mulavara, Ajitkumar↗
NASA NTRS2012

HyDE Framework for Stochastic and Hybrid Model-Based Diagnosis

Hybrid Diagnosis Engine (HyDE) is a general framework for stochastic and hybrid model-based diagnosis that offers flexibility to the diagnosis application designer. The HyDE architecture supports the use of multiple modeling paradigms at the component and system level. Several alternative algorithms are available for the various steps in diagnostic reasoning. This approach is extensible, with support for the addition of new modeling paradigms as well as diagnostic reasoning algorithms for existing or new modeling paradigms. HyDE is a general framework for stochastic hybrid model-based diagnosis of discrete faults; that is, spontaneous changes in operating modes of components. HyDE combines ideas from consistency-based and stochastic approaches to model- based diagnosis using discrete and continuous models to create a flexible and extensible architecture for stochastic and hybrid diagnosis. HyDE supports the use of multiple paradigms and is extensible to support new paradigms. HyDE generates candidate diagnoses and checks them for consistency with the observations. It uses hybrid models built by the users and sensor data from the system to deduce the state of the system over time, including changes in state indicative of faults. At each time step when observations are available, HyDE checks each existing candidate for continued consistency with the new observations. If the candidate is consistent, it continues to remain in the candidate set. If it is not consistent, then the information about the inconsistency is used to generate successor candidates while discarding the candidate that was inconsistent. The models used by HyDE are similar to simulation models. They describe the expected behavior of the system under nominal and fault conditions. The model can be constructed in modular and hierarchical fashion by building component/subsystem models (which may themselves contain component/ subsystem models) and linking them through shared variables/parameters. The component model is expressed as operating modes of the component and conditions for transitions between these various modes. Faults are modeled as transitions whose conditions for transitions are unknown (and have to be inferred through the reasoning process). Finally, the behavior of the components is expressed as a set of variables/ parameters and relations governing the interaction between the variables. The hybrid nature of the systems being modeled is captured by a combination of the above transitional model and behavioral model. Stochasticity is captured as probabilities associated with transitions (indicating the likelihood of that transition being taken), as well as noise on the sensed variables.

Narasimhan, Sriram↗
NASA NTRS2014

Improving Sensorimotor Function and Adaptation using Stochastic Vestibular Stimulation

Astronauts experience sensorimotor changes during adaption to G-transitions that occur when entering and exiting microgravity. Post space flight, these sensorimotor disturbances can include postural and gait instability, visual performance changes, manual control disruptions, spatial disorientation, and motion sickness, all of which can hinder the operational capabilities of the astronauts. Crewmember safety would be significantly increased if sensorimotor changes brought on by gravitational changes could be mitigated and adaptation could be facilitated. The goal of this research is to investigate and develop the use of electrical stochastic vestibular stimulation (SVS) as a countermeasure to augment sensorimotor function and facilitate adaptation. For this project, SVS will be applied via electrodes on the mastoid processes at imperceptible amplitude levels. We hypothesize that SVS will improve sensorimotor performance through the phenomena of stochastic resonance, which occurs when the response of a nonlinear system to a weak input signal is optimized by the application of a particular nonzero level of noise. In line with the theory of stochastic resonance, a specific optimal level of SVS will be found and tested for each subject [1]. Three experiments are planned to investigate the use of SVS in sensory-dependent tasks and performance. The first experiment will aim to demonstrate stochastic resonance in the vestibular system through perception based motion recognition thresholds obtained using a 6-degree of freedom Stewart platform in the Jenks Vestibular Laboratory at Massachusetts Eye and Ear Infirmary. A range of SVS amplitudes will be applied to each subject and the subjectspecific optimal SVS level will be identified as that which results in the lowest motion recognition threshold, through previously established, well developed methods [2,3,4]. The second experiment will investigate the use of optimal SVS in facilitating sensorimotor adaptation to system disturbances. Subjects will adapt to wearing minifying glasses, resulting in decreased vestibular ocular reflex (VOR) gain. The VOR gain will then be intermittently measured while the subject readapts to normal vision, with and without optimal SVS. We expect that optimal SVS will cause a steepening of the adaptation curve. The third experiment will test the use of optimal SVS in an operationally relevant aerospace task, using the tilt translation sled at NASA Johnson Space Center, a test platform capable of recreating the tilt-gain and tilt-translation illusions associated with landing of a spacecraft post-space flight. In this experiment, a perception based manual control measure will be used to compare performance with and without optimal SVS. We expect performance to improve in this task when optimal SVS is applied. The ultimate goal of this work is to systematically investigate and further understand the potential benefits of stochastic vestibular stimulation in the context of human space flight so that it may be used in the future as a component of a comprehensive countermeasure plan for adaptation to G-transitions.

Galvan, R. C.↗
DOE OSTI2025

Assimilating partial observation to enhance feedback control of stochastic dynamical systems

Here, in this paper, we present a novel methodology to tackle feedback optimal control problems in scenarios where the exact state of the controlled process is unknown. It integrates data assimilation techniques and optimal control solvers to manage partial observation of the state process, a common occurrence in practical scenarios. Traditional stochastic optimal control methods assume full state observation, which is often not feasible in real-world fluid dynamics control problems. Our approach underscores the significance of utilizing observational data to inform control policy design. Specifically, we introduce a kernel learning backward stochastic differential equation (SDE) filter to enhance data assimilation efficiency and propose a sample-wise stochastic optimization method within the stochastic maximum principle framework. We demonstrate the efficacy and accuracy of our method in the control of advection-diffusion-reaction flow problem and the Dubins airplane maneuvering problem with model uncertainty.

data driven↗
DOE OSTI2025

The tensor-train stochastic finite volume method for uncertainty quantification

The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. Here, we introduce the stochastic finite volume method within the tensor-train framework to counteract this limitation. This integration, however, comes with its own set of difficulties, mainly due to the propensity for shock formation in hyperbolic systems. To overcome these issues, we have developed a tensor-train-adapted stochastic finite volume method that employs a global WENO reconstruction, making it suitable for such complex systems. This approach represents the first step in designing tensor-train techniques for hyperbolic systems and conservation laws involving shocks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Coexistence of Synchronization and Stochasticity in Thermally Coupled Mott Oscillators

Synchronization is conventionally regarded as a mechanism for suppressing variability and enforcing order in coupled systems, from pendula and lasers to neurons and electronic oscillators. Here, we show that synchronization can also embed stochasticity at finer scales. We observe this phenomenon in thermally coupled VO 2 neuristors, where robust in-phase synchronization at the microsecond scale coexists with spike onset fluctuations at the nanosecond scale, with no fixed leader. The coexistence of order and disorder originates from stochastic domain-level physics of the insulator–metal and metal–insulator transitions, where local variations in transition temperature drive cycle-to-cycle randomness in nucleation, percolation, and relaxation. A stochastic domain model reproduces this effect by generating synchronized spike trains with random lead–lag jitter, and experimental interspike interval statistics confirm the persistence of fine-scale variability despite macroscopic phase locking. These findings establish that synchronization and stochasticity can coexist within the same physical platform, revealing hidden disorder within collective order. Furthermore, this insight reframes synchronization as not purely deterministic, but as a universal context where microscopic variability can persist, with implications for electronics, cryptography, and the fundamental physics of order–disorder coexistence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Using intrusive approaches as a step towards accounting for stochasticity in wind turbine design

Current wind turbine design methods require tens of thousands of time-domain simulations and use different random seeds to account for the stochasticity of the environmental conditions. The account of stochasticity is nonintrusive because the sampling method calls a deterministic model multiple times without changing its underlying equations. In this work, we investigate and demonstrate using simple proof of concepts how intrusive approaches can be used to directly account for stochasticity in the equations representing a mechanical system. Our long term goal is to apply such methodology to the design of wind turbines without requiring an excessive number of simulations. Intrusive methods manipulate stochastic variables directly to provide the probability density functions (PDFs) of the states and outputs at any time as functions of the PDFs of the inputs. We illustrate how different methods can be used with a reduced-order model of a wind turbine with one degree of freedom and for linear and nonlinear models. We discuss how the methods can be extended and what it will take to apply them to a level of fidelity similar to current state-of-the-art wind turbine design tools.

17 WIND ENERGY↗
DOE OSTI2024

Stochastic Trust-Region Algorithm in Random Subspaces with Convergence and Expected Complexity Analyses

Here, this work proposes a framework for large-scale stochastic derivative-free optimization (DFO) by introducing STARS, a trust-region method based on iterative minimization in random subspaces. This framework is both an algorithmic and theoretical extension of a random subspace derivative-free optimization (RSDFO) framework, and an algorithm for stochastic optimization with random models (STORM). Moreover, like RSDFO, STARS achieves scalability by minimizing interpolation models that approximate the objective in low-dimensional affine subspaces, thus significantly reducing per-iteration costs in terms of function evaluations and yielding strong performance on largescale stochastic DFO problems. The user-determined dimension of these subspaces, when the latter are defined, for example, by the columns of so-called Johnson-Lindenstrauss transforms, turns out to be independent of the dimension of the problem. For convergence purposes, inspired by the analyses of RSDFO and STORM, both a particular quality of the subspace and the accuracies of random function estimates and models are required to hold with sufficiently high, but fixed, probabilities. Using martingale theory under the latter assumptions, an almost sure global convergence of STARS to a first-order stationary point is shown, and the expected number of iterations required to reach a desired first-order accuracy is proved to be similar to that of STORM and other stochastic DFO algorithms, up to constants.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Stochastic fracture generation and thermo-hydro-mechanical modeling in an equivalent continuum framework for enhanced geothermal systems

Enhanced geothermal systems (EGS) involve fracturing low permeability material to establish well connectivity and then injecting and circulating fluid into the fractured subsurface for geothermal power production. Changes in fracture aperture from contraction of the cooling matrix rock may alter network connectivity and risk thermal short-circuiting. Thermo-hydro-mechanical (THM) models are a useful tool to study these processes. However, as fracture networks are complex, and data may be limited, fracture networks in THM models are often stochastically generated. Given reliance on stochastic fracture networks and THM modeling to represent the subsurface and assess productivity of EGS, increased understanding of the influence of such statistically derived fracture networks on flow and heat transport in THM models is needed. Here, a new fracture process model is developed in the reactive transport code PFLOTRAN to stochastically generate fracture families and simulate changes in fracture aperture over time due to temperature changes of the rock matrix. Sixty-four different fracture networks ranging from well to poorly-connected, are modeled in PFLOTRAN with and without mechanical processes (THM vs TH). Results indicate that for well-connected fracture networks, thermal short-circuiting is less of a concern due to the abundance of available alternative flowpaths. For poorly-connected fracture networks, inclusion of mechanical processes showed steep thermal drawdown coincident with increase in fracture aperture along developing colder flowpaths, demonstrating the risk of thermal short-circuiting. Simulations with additional, larger fractures engineered to establish connectivity in a poorly-fractured subsurface, indicate that while stochastic variation of fracture orientation of the background network had limited influence, such variation in the engineered fractures significantly affected flow and heat transport.

Discrete fracture networks (DFN)↗
DOE OSTI2024

Stochastic Optimization and Uncertainty Quantification of Natrium-based Nuclear-Renewable Energy Systems for Flexible Power Applications in Deregulated Markets

Rapid integration of variable renewable energy sources (VRES) has made modeling and stochastic optimization of hybrid energy systems crucial for studying their long-term performance and viability. However, most studies have focused on just historical data, which may be unreliable for capturing short-term fluctuations, rare events, and long-term patterns of energy demand, price, and the variability of renewable energy sources. For this study, optimal synthetic time series models were developed using Wasserstein distance. The models were validated by comparing the key statistical measures against those of the historical data. They were then used to optimize the integrated Natrium-style advanced energy systems and their long-term (30 years) economics. The stochastic model performs bi-level optimization to find the optimal sizes for the balance of plant and thermal energy storage, while also optimizing energy dispatch to achieve the maximum net present value. In studies of two deregulated markets (California ISO and the Electric Reliability Council of Texas), the integrated Natrium-style system performed better in CAISO than in ERCOT, given higher and more consistent electricity prices during peak-demand periods. The potentially enlarged cost associated with the variable operation and maintenance of the TES system also plays a significant role in driving the system sizing, thus its impacts on the system are investigated in detail through comparison against a baseline case. The study also finds that the bi-level optimization results based on stochastic gradient descent closely match the grid search results. The uncertainty quantification of the stochastic signals provides further NPV-related insights and probability distributions for the case studies. The normal standard error of the mean of NPV for the case with and without TES VOM for CAISO were found to be 7.73M (plus-minus sign) 1.09M USD and 104.99M (plus-minus sign) 1.25M USD, respectively based on a 95% confidence. Given the relatively small NPV variance based on 150 samples, the analysis affords the most robust possible prediction of the techno-economic performance of the integrated Natrium-style energy systems.

25 ENERGY STORAGE↗
DOE OSTI2024

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories

Here, the accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH 3 ) molecule and the nucleophilic substitution (S N 2) reaction F – + CH 3 F → FCH 3 + F – . We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Iyer, Gopal R.↗
DOE OSTI2025

Derivative-free stochastic optimization via adaptive sampling strategies

In this paper, we present a novel derivative-free framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning to quantum computing involve settings where only stochastic function values are obtained via a zeroth-order oracle, which has no available gradient information and necessitates the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and integrating adaptive sampling techniques to control the accuracy in these stochastic approximations. Our framework encapsulates several gradient estimation techniques, including standard finite-difference, Gaussian smoothing, sphere smoothing, randomized coordinate finite-difference, and randomized subspace finite-difference methods. We provide theoretical convergence guarantees for our framework and analyze the worst-case iteration and sample complexities associated with each gradient estimation method. Finally, we demonstrate the empirical performance of the methods on logistic regression and nonlinear least squares problems.

Adaptive sampling↗