Search NASA⌕ Search

SEARCH · Search NASA

Results for “Numerical optimization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 559 records · Page 31

Self-consistent mean-field quantum approximate optimization

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗

Physics-Informed Graph Neural Networks for Collaborative Dynamic Reconfiguration and Voltage Regulation in Unbalanced Distribution Systems

Network reconfiguration has long been employed as a strategic approach to minimize power distribution system losses and effectively regulate voltage levels. Tap-changing voltage regulators are also critical for controlling bus voltages, especially in accommodating the increasing integration of distributed energy resources (DERs) with intermittent outputs. This paper introduces novel methodologies to address the challenges of dynamic reconfiguration and optimal tap setting in unbalanced three-phase distribution systems. We propose an approximated mixed-integer quadratically constrained program (MIQCP) to model dynamic reconfiguration, along with a pioneering formulation for voltage regulator (VR) tap-setting based on Special Ordered Set type 1 (SOS1). To mitigate computational complexity, we propose a physics-informed spatial-temporal graph convolutional network (STGCN) with an integrated link classifier. The proposed approach enables efficient solution generation by fixing specific variables in the MIQCP instance and solving the simplified sub-MIP using an MIP solver. Numerical studies demonstrate the superior prediction accuracy of our STGCN model compared to baseline neural network models, resulting in reduced DER curtailment and voltage deviation with shorter computation time.

dynamic reconfiguration↗

Resource Characterization for Community Scale Tidal Instream Energy in Maine [Abstract]

Coastal and island communities in Maine are seeking solutions to increase the resiliency of their electrical grid while also reducing their carbon footprint. Unfortunately, many community scale tidal resources identified on the Maine coast have not been rigorously evaluated; previous studies identified numerous hot spots but left many of them unevaluated or under evaluated (e.g., only power density was assessed in many cases). The primary objective of this TEAMER project is to evaluate selected community scale tidal instream resources to demonstrate their potential for contributing to the renewable energy needs of nearby coastal communities. The methods developed in this study will enable the total community scale tidal instream energy resource along the Maine coast to be evaluated in follow-on studies. The study will also enable turbine developers to understand how to scale and optimize their devices for deployment in turbine farms at community scale sites. Data from the study will be shared publicly through MHKDR or relevant community websites.

16 TIDAL AND WAVE POWER↗

An impermeable copper surface monolayer with high-temperature oxidation resistance

Despite numerous efforts involving surface coating, doping, and alloying, maintaining surface stability of metal at high temperatures without compromising intrinsic properties has remained challenging. Here, we present a pragmatic method to address the accelerated oxidation of Cu, Ni, and Fe at temperatures exceeding 200 °C. Inspired by the concept that oxygen (O) itself can effectively obstruct the pathway of O infiltration, this study proposes the immobilization of O on the metal surface. Through extensive calculations considering various elements (C, Al, Si, Ge, Ga, In, and Sn) to anchor O on Cu surfaces, Si emerges as the optimal element. The theoretical findings are validated through systematic sputtering deposition experiments. The introduction of anchoring elements to reinforce Cu–O bonds enables the formation of an atomically thin barrier on the Cu surface, rendering it impermeable to O even at high temperatures (400 °C) while preserving its intrinsic conductivity. This oxidation resistance, facilitated by the impermeable atomic monolayer, opens promising opportunities for researchers and industries to overcome limitations associated with the use of oxidizable metal films.

36 MATERIALS SCIENCE↗

Leveraging a Neural Network-Enhanced Reproducing Kernel Particle Method for Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation has been developed to analyze this system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. Here, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RKPM is additionally used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

degradation↗

Lieb-Mattis States for Robust Entangled Differential Phase Sensing

We explore a two-node, entanglement-enhanced sensor network for differential phase sensing that exploits decoherence-free subspaces to suppress common-mode noise, a primary limitation of many state-of-the-art quantum sensors. We identify a class of entangled states that, while not strictly optimal, achieve the same asymptotic sensitivity scaling as optimal states and can be prepared efficiently from initially unentangled atomic ensembles. Importantly, the preparation time decreases with increasing system size, which makes the states compatible with realistic noise processes in present-day quantum sensors that operate with large particle numbers but lack full error correction. We illustrate these ideas using two cavity-mediated preparation protocols: (i) coherent, unitary entanglement generation analogous to bosonic two-mode squeezing, yielding Heisenberg scaling, and (ii) dissipative preparation through collective emission into a shared cavity mode, providing a square-root improvement beyond the standard quantum limit. Numerical simulations show that both approaches remain effective at experimentally realistic cavity cooperativities, establishing a practical path toward scalable, quantum-enhanced differential phase sensing.

Kaubruegger, Raphael [National Institute of Standa↗

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms

The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters, which is usually done using a variational optimization loop. Parameter transfer, or parameter concentration, is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. In this work, we systematically study QAOA parameter transferability from small problem sizes (16 and 27 decision variables) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool \texttt{JuliQAOA} to perform classical angle finding for up to $49$ QAOA layers ($p$). Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States (PEPS), Matrix Product State (MPS), and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to other (unseen) problem instances does not in general provide monotonically improving performance as a function of $p$ - there are many cases where the performance temporarily decreases as a function of $p$ - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the $100+$ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of transfer-learned QAOA parameters on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to $p=5$ on \texttt{ibm\_fez}, up to $p=9$ on \texttt{ibm\_torino}, and up to $p=10$ on \texttt{ibm\_pittsburgh}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Development of fiber orientation in injection molding: Comparison of glass fiber, carbon fiber and their hybrid composites

Fiber orientation distribution (FOD) in injection-molded panels with respect to distance from the gate was analyzed using X-ray computed tomography (X-CT) for glass fiber (GF), carbon fiber (CF), and hybrid CF/GF (CGF) reinforced nylon 66. To understand the reason behind the FOD with different fiber types, computational fluid dynamics (CFD) and rheology were performed. Samples were extracted at three locations: near the gate, center, and opposite end. Thickness of the layers of typical skin-shell-core type FOD varied with fiber type and location. GF achieved flow direction alignment (in shell) earlier than viscous CF and CGF near the gate, whereas CF showed the highest flow-direction alignment at the center due to shear induced orientation. At the opposite end, GF experienced more backflow than others indicating faster mold filling owing to its lower viscosity. Hybrid CGF exhibited GF-dominated center and CF-dominated end region. The numerical model used to obtain FOD and rheological predictions for the CF and GF composites served to corroborate the trends observed in the experimental trials. The FOD responses across fiber types and location were reflected in their longitudinal and transverse properties. Only GF showed higher longitudinal modulus over transverse modulus near the gate attributed to rapid alignment, whereas CF and CGF exhibited opposite trend. However, fountain flow enhanced the longitudinal modulus over transverse modulus with the distance for all, particularly for CF. This study offers insights into mold filling behavior of different fibers which are critical in optimizing injection molding conditions for tailored final properties.

36 MATERIALS SCIENCE↗

Thermodynamic modeling of countercurrent chemical looping reverse water gas shift process for redox material screening

The reverse water gas shift (RWGS) reaction is a key pathway for CO 2 utilization, particularly within Power-to-X process chains aimed at sustainable fuel and chemical production. Countercurrent chemical looping (CL-RWGS) using non-stoichiometric oxides can overcome equilibrium limitations of conventional RWGS reactors, enabling significantly higher CO 2 conversions. However, modeling the limiting performance of such systems is challenging due to their multiphase nature and coupled spatial and temporal variation in chemical composition. In this work, we present a discretized batch equilibrium model that simulates CL-RWGS reactors as a series of localized equilibrium exchanges between gas and solid elements. The model is numerically stable, computationally efficient, and free of kinetic source terms, making it well-suited for parametric studies and system-level integration. It is validated against established convection–diffusion models and shown to predict reasonable upper bounds on experimental results. Application of the model to a range of oxygen carrier materials identifies cerium–zirconium solid solutions, particularly Ce 0.80 Zr 0.20 O 2 , as a promising class offering superior oxygen storage characteristics compared to state-of-the-art La 0.6 Sr 0.4 FeO 3 . This framework provides a robust platform for materials screening, reactor sizing, and performance optimization in chemical looping systems. The model implementation is available as open-source software to support further research and development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

Rahman, Md Sadman Sakib [University of California,↗

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗

Solar-Tracker Diffuse-Response Algorithm for Balancing Energy Gain and Mechanical Wear in Photovoltaic Systems

Single-axis solar tracking maximizes photovoltaic energy production under clear-sky conditions; however, its effectiveness decreases under cloudy and overcast skies, where diffuse irradiance dominates and the optimal module orientation changes. Conventional tracking algorithms either neglect sky conditions or rely on simplified diffuse-response strategies that may trigger frequent tracker repositioning under variable cloud cover, leading to increased mechanical wear with marginal energy gains. This work proposes an enhanced diffuse-response tracking algorithm that explicitly accounts for both the intensity and temporal persistence of cloudiness. By requiring overcast conditions to persist for a minimum duration before reorienting the tracker to a diffuse-stow position, the proposed approach reduces unnecessary movements while preserving the benefits of diffuse-response operation. The algorithm is evaluated through numerical simulations based on historical meteorological data and validated using field measurements on monofacial and bifacial photovoltaic strings. The results show that the proposed strategy reduces excess tracker movement from 114% to 0.16% while maintaining nearly the same energy yield. Compared to a conventional diffuse-response algorithm, the associated energy reduction is minimal (≈0.17%) relative to the ≈0.37% yield gain observed at the studied location. These findings demonstrate that incorporating cloudiness duration enables a practical compromise between energy performance and tracker durability, particularly for monofacial photovoltaic systems.

14 SOLAR ENERGY↗

FEM Analysis of Hybrid LTS/HTS Cos-Theta Dipole Magnet

After the recent results on Bi-2212 superconductive magnets realized and tested in canted cosine-theta and solenoid designs, respectively, at Lawrence Berkeley National Laboratory (LBNL) and NHMFL, the first Bi-2212 stress-managed cosine-theta insert magnet is in the assembly phase at Fermilab. This insert will be part of the first hybrid cosine-theta magnet made of Nb3Sn outer layers within the US-MDP effort to reach 20 T bore field. This paper reports the analytical analysis of the cosine-theta Nb3Sn/Bi-2212 hybrid magnet. As an introduction, it shows the validation of the finalized HTS coils' design optimized using the ROXIE code. Subsequently, it reports the parameters, logic, and implementation method of the 2D electromagnetic and mechanical FEM analysis of the LTS/HTS hybrid magnet. Results from the ANSYS detailed model made with sub-modeling geometry are compared with the homogeneous model implemented in the past. Moreover, a Python code was implemented to simulate the current degradation due to stresses in the detail-modeled conductor areas. The current degradation is introduced in the simulation dynamics for both conductors as an iteration process during the energization load step only after applying pre-stress and thermal loads. The numerical and graphic results of the 2D cosine-theta LTS/HTS magnet cross-section will be described and analyzed.

D'Agliano, A.↗

Application-specific machine-learned interatomic potentials: exploring the trade-off between DFT convergence, MLIP expressivity, and computational cost

Machine-learned interatomic potentials (MLIPs) are revolutionizing computational materials science and chemistry by offering an efficient alternative to ab initio molecular dynamics (MD) simulations. However, fitting high-quality MLIPs remains a challenging, time-consuming, and computationally intensive task where numerous trade-offs have to be considered, e.g., How much and what kind of atomic configurations should be included in the training set? Which level of ab initio convergence should be used to generate the training set? Which loss function should be used for fitting the MLIP? Which machine learning architecture should be used to train the MLIP? The answers to these questions significantly impact both the computational cost of MLIP training and the accuracy and computational cost of subsequent MLIP MD simulations. In this study, we use a configurationally diverse beryllium dataset and quadratic spectral neighbor analysis potential. We demonstrate that joint optimization of energy versus force weights, training set selection strategies, and convergence settings of the ab initio reference simulations, as well as model complexity can lead to a significant reduction in the overall computational cost associated with training and evaluating MLIPs. This opens the door to computationally efficient generation of high-quality MLIPs for a range of applications which demand different accuracy versus training and evaluation cost trade-offs.

36 MATERIALS SCIENCE↗

Precision Reconstruction of Rational Conformal Field Theory from Exact Fixed-Point Tensor Network

The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real-space renormalization group (RG) scheme. Numerically approximate fixed-point (FP) tensors are widely used to extract the conformal data of the underlying conformal field theory (CFT) describing critical phenomena. In this paper, we present an explicit analytical construction of the FP tensor for 2D rational CFT. We define it as a correlation function between the “boundary-changing operators” (BCO) on triangles. Our construction fully captures all the real-space RG conditions. We also provide concrete examples, such as Ising, Yang-Lee, and tricritical Ising models, to compute the scaling dimensions explicitly based on the corresponding FP tensor. The BCO descendants turn out to be an optimal basis such that truncation in bond dimensions naturally produces comparable accuracies with the leading existing FP algorithms. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture naturally emerges. Our results also open a new door toward understanding CFT in higher dimensions. Published by the American Physical Society 2025

Cheng, Gong (ORCID:0009000891587404)↗

Optimizing enzymes for plastic upcycling using machine learning design and high throughput experiments

Plastic use is ubiquitous in the modern world, and polyethylene terephthalate (PET) is one of the most abundantly produced plastics (and the most highly produced polyester), with ~65 million metric tons manufactured annually. To the consumer, PET is likely most recognizable as the plastic used to make beverage bottles. Like many plastics, traditional mechanical or chemical means of PET deconstruction and upcycling are costly and inefficient. Because of these challenges, recycled plastic is generally of lower quality and is more expensive to produce than virgin plastic derived from petroleum. Ultimately, this results in most plastic ending up as waste. We view plastic waste as an underutilized resource which, with the development of more efficient and high-quality recycling processes, could (1) generate significant economic value while (2) decreasing petroleum usage and greenhouse gas emissions, as well as (3) minimizing its negative environmental and health impacts. Biocatalytic recycling, or biomanufacturing the basic building blocks of new plastic from plastic waste, is a promising approach to plastic reuse that complements existing recycling technologies. Recently, biological enzymes capable of breaking down PET have garnered significant attention as an attractive means of dealing with the plastic problem. These enzymes are currently undergoing pilot studies for implementation in industrial-scale enzyme-based recycling. However, there are significant limitations to current enzymes, including the need to perform costly pre-processing of the plastic waste before the enzymes are able to work. Further optimization of these enzymes is necessary to make these technologies competitive, and ultimately incentivise industry-wide adoption of this biology-based green recycling technology. n this work we demonstrate a means to design and generate performant biological enzymes, capable of efficiently deconstructing plastic waste. Specifically, we applied recent advances in artificial intelligence, machine learning, and statistical analysis to design new versions and discover natural enzymes capable of breaking down PET. We focused on optimizing key properties that are important for industrial-scale enzymatic recycling such as pH and thermotolerance. Normal testing of enzymatic plastic-deconstruction is extremely labor intensive and so through this work we also developed a robotic-assisted experimental pipeline capable of characterizing thousands of candidate enzymes. The results of this iterative, AI-guided, multi-discipline approach have led to increases in enzymatic breakdown of over 150X over starting enzymes. This work supports the rapidly developing and transformative field of biocatalytic solutions to environmental problems beyond the discovery and predictive understanding of enzymes for polymer recycling, and has wide implications for tackling numerous energy problems such as carbon capture and fixation (e.g., engineering carbon monoxide dehydrogenase and the rubisco-pathway), biomining (e.g., design of lanthanide-binding proteins) and biomanufacturing (e.g., lignin-deconstruction enzymes).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

Lu, Yao [Yale U.; Yale U. (main); Fermilab] (ORCID↗

Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-like Calculations

Here, this Letter introduces a unified emulation framework for studying continuum physics in finite quantum systems. Using a reduced basis method, we construct powerful emulators for the inhomogeneous Schrödinger equation that operate in a combined parameter space of complex energy (𝐸) and other inputs (𝜽). Within the space, the emulators simultaneously perform analytical continuation in 𝐸—extracting continuum physics from numerically simpler bound-state-like calculations—and interpolate this entire process across 𝜽. This yields a small, non-Hermitian system whose properties (e.g., resonances and scattering observables) can be rapidly predicted for any 𝜽. Crucially, the complex-𝐸 emulation provides a pathway to compute continuum observables for complex systems where advanced bound-state methods exist but direct continuum calculations are yet to be developed, while the 𝜽 emulation enables rapid parameter-space exploration and can be adapted to accelerate other existing continuum calculations. Demonstrations with two- and three-body systems highlight the method’s effectiveness and suggest its connection to (near-)optimal rational approximation. This Letter presents the key results, with further details reserved for a companion paper.

ab initio calculations↗