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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Active Suspension Parameters Identification: An Algebraic Approach and its Application to Suspension Travel Control

The parameters of an active suspension need to be identified online, such that the suspension control system can be adapted to mechanical wear and load change. Recursive least squares and observer-based methods are frequently utilized to fulfill this purpose. However, they can yield slow parameter identification due to their asymptotic nature. We propose an algebraic identifier to estimate the parameters of an active suspension online, which does not maintain an asymptotic convergence phase. Simulation results demonstrate the effectiveness of the proposed algebraic approach.

Wang, Zejiang↗
DOE OSTI2019

A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows

This paper presents a comparison of parallel strong scaling performance of classical and aggregation algebraic multigrid (AMG) preconditioners in the context of wind turbine simulations. Fluid motion is governed by the incompressible Navier--Stokes equations, discretized in space with control-volume finite elements and in time with an inexact projection scheme using an implicit integrator. A discontinuous-Galerkin sliding-mesh algorithm captures rotor motion. The momentum equations are solved with iterative Krylov methods, preconditioned by symmetric Gauss--Seidel (SGS) in Trilinos and $\ell_1$ SGS in hypre. The mass-continuity equation is solved with GMRES preconditioned by AMG and can account for the majority of simulation time. Reducing this continuity solve time is crucial. Wind turbine simulations present two unique challenges for AMG preconditioned solvers: the computational meshes include strongly anisotropic elements, and mesh motion requires matrix reinitialization and computation of preconditioners at each time step. Detailed timing profiles are presented and analyzed, and best practices are discussed for both classical and aggregation-based AMG. Results are presented for simulations of two different wind turbines with up to 6 billion grid points on two different computer architectures. For moving mesh problems that require linear-system reinitialization, the well-established strategy of amortizing preconditioner setup costs over a large number of time steps to reduce the solve time is no longer valid. Instead, results show that faster time to solution is achieved by reducing preconditioner setup costs at the expense of linear-system solve costs. Standard smoothed aggregation with Chebyshev relaxation was found to perform poorly when compared with classical AMG in terms of solve time and robustness. However, plain aggregation was comparable to classical AMG.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Reducing communication in algebraic multigrid with multi-step node aware communication

Algebraic multigrid (AMG) is often viewed as a scalable [Formula: see text] solver for sparse linear systems. Yet, AMG lacks parallel scalability due to increasingly large costs associated with communication, both in the initial construction of a multigrid hierarchy and in the iterative solve phase. This work introduces a parallel implementation of AMG that reduces the cost of communication, yielding improved parallel scalability. It is common in Message Passing Interface (MPI), particularly in the MPI-everywhere approach, to arrange inter-process communication, so that communication is transported regardless of the location of the send and receive processes. Performance tests show notable differences in the cost of intra- and internode communication, motivating a restructuring of communication. In this case, the communication schedule takes advantage of the less costly intra-node communication, reducing both the number and the size of internode messages. Node-centric communication extends to the range of components in both the setup and solve phase of AMG, yielding an increase in the weak and strong scaling of the entire method.

Computer Science↗
DOE OSTI2026

Commutative Algebra Modeling in Materials Science – A Case Study on Metal–Organic Frameworks (MOFs)

Metal-organic frameworks (MOFs) are a class of important crystalline and highly porous materials whose hierarchical geometry and chemistry hinder interpretable predictions in materials properties. Commutative algebra is a branch of abstract algebra that has been rarely applied in data and material sciences. We introduce the first ever commutative algebra modeling and prediction in materials science. Specifically, category-specific commutative algebra (CSCA) is proposed as a new framework for MOF representation and learning. It integrates element-based categorization with multiscale algebraic invariants to encode both local coordination motifs and global network organization of MOFs. These algebraically consistent, chemically aware representations enable compact, interpretable, and data efficient modeling of MOF properties such as Henry’s constants and uptake capacities for common gases. Compared to traditional geometric and graph-based approaches, CSCA achieves comparable or superior predictive accuracy while substantially improving interpretability and stability across data sets. By aligning commutative algebra with the chemical hierarchy, the CSCA establishes a rigorous and generalizable paradigm for understanding structure and property relationships in porous materials and provides a nonlinear algebra-based framework for data-driven material discovery.

Khaemba, Caleb S.↗
DOE OSTI2021

A High Performance Sparse Tensor Algebra Compiler in MLIR

Sparse tensor algebra is widely used in many applications, including scientific computing, machine learning, and data analytics. The performance of sparse tensor algebra kernels strongly depends on the intrinsic characteristics of the input tensors, hence many storage formats are designed for tensors to achieve optimal performance for particular applications/architectures, which makes it challenging to implement and optimize every tensor operation of interest on a given architecture. We propose a tensor algebra domain-specific language (DSL) and compiler framework to automatically generate kernels for mixed sparse-dense tensor algebra operations. The proposed DSL provides high-level programming abstractions that resemble the familiar Einstein notation to represent tensor algebra operations. The compiler introduces a new Sparse Tensor Algebra dialect built on top of LLVM's extensible MLIR compiler infrastructure for efficient code generation while covering a wide range of tensor storage formats. Our compiler also leverages input-dependent code optimization to enhance data locality for better performance. Our results show that the performance of automatically generated kernels outperforms the state-of-the-art sparse tensor algebra compiler, with up to 20.92x, 6.39x, and 13.9x performance improvement over state-of-the-art tensor algebra compilers, for parallel SpMV, SpMM, and TTM, respectively.

Tian, Ruiqin↗
DOE OSTI2019

Chiral algebras of two-dimensional SYK models

We study chiral algebras in the $\bar{Q}$-cohomology of two dimensional SYK models with extended supersymmetry. In a special limit discovered in [1], we are able to construct explicitly a “vertical” single-particle higher-spin algebra that is bilinear in the fundamental fields. This algebra can be regarded as the counterpart, when going away from criticality, of the infrared emergent higher-spin symmetry of the N=(0,2) SYK model. Moreover, a second “horizontal” single-particle higher-spin algebra appears in this limit. Together with the vertical algebra they generate a stringy algebra with a “higher spin square” structure that is believed to appear in the tensionless limit of string theory. On the other hand, we do not find single-particle higher-spin algebra away from the special limit, which is consistent with the result in [1]. Our analysis is carried out for each individual realization of the random couplings and for finite N (and M), which in particular indicates that the conclusion in [1] is robust to 1/N corrections.

1/N expansion↗
DOE OSTI2021

Next-to-$\mathrm{MHV}$ Yang-Mills kinematic algebra

Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open problem that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closed-form expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

CAML: Commutative Algebra Machine Learning─A Case Study on Protein–Ligand Binding Affinity Prediction

Recently, Suwayyid and Wei introduced commutative algebra as an emerging paradigm for machine learning and data science. In this work, we propose commutative algebra machine learning (CAML) for the prediction of protein−ligand binding affinities. Specifically, we apply persistent Stanley−Reisner theory, a key concept in combinatorial commutative algebra, to the affinity predictions of protein−ligand binding and metalloprotein−ligand binding. We present three new algorithms, i.e., element-specific commutative algebra, category-specific commutative algebra, and commutative algebra on bipartite complexes, to tackle the complexity of data involved in (metallo) protein−ligand complexes. We show that the proposed CAML outperforms other state-of-theart methods in (metallo) protein−ligand binding affinity predictions, indicating the great potential of commutative algebra learning.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Enabling Efficient Sparse Computations using Linear Algebra Aware Compilers

This project developed the LAPIS compiler framework, built on the Multilevel Intermediate Representation (MLIR), to optimize sparse linear algebra operations and support performance portability across diverse architectures. The main innovation of LAPIS is the Kokkos dialect, which allows for lowering codes from a high productivity language to different architectures in an elegant way. The dialect also allows the conversion of lower-level MLIR code to C++ Kokkos code, facilitating the integration of scientific machine learning (SciML) models into applications. To extend LAPIS for distributed memory architectures, a new partition dialect was created to manage the distribution of sparse tensors and express communication patterns for sparse linear algebra operations. This dialect also supports the distributed execution of operators and includes algorithmic optimizations to minimize communication to improve performance. The project also demonstrates that MLIR can enable effective linear algebra-level optimizations, improving performance on different GPUs for both sparse and dense linear algebra kernels. Key applications of LAPIS include sparse linear algebra and graph kernels, TenSQL, a relational database management solution built on GraphBLAS, and the development of subgraph isomorphism and monomorphism kernels, showcasing performance portability. In summary, the LAPIS framework supports productivity, performance, portability, and distributed memory execution, while also enabling linear algebra-level optimizations that are challenging in traditional programming languages, with successful applications ranging from simple sparse linear algebra to complex graph kernels.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The algebraic structure of gravitational scrambling

We introduce a new algebraic framework to describe gravitational scrambling, including the semiclassical limit of any out-of-time-order correlation function that is built out of operator insertions separated by approximately the scrambling time. In two dimensions, the scrambling algebra, which we call a modular-twisted product, is defined in terms of two copies of the Leutheusser-Liu half-sided modular inclusion of von Neumann algebras; these describe early- and late-time operators respectively. In limits where the separation between insertions is taken to be either significantly greater or smaller than the scrambling time, the modular-twisted product reduces, respectively, to free- and tensor-product algebras that were previously studied in [arXiv:2209.10454]. In a sense, the modular-twisted product interpolates between these two products. Including the Hamiltonian in the scrambling algebra leads to a Type II$_\infty$ von Neumann algebra with finite renormalized entropies that interpolate between single-QES and multi-QES phases. We also describe how to generalize the modular-twisted product algebra to higher dimensions, including spatially localized boundary excitations.

FOS: Physical sciences↗
DOE OSTI2025

Analyzing the Quantum Approximate Optimization Algorithm: Ansätze, Symmetries, and Lie Algebras

The quantum approximate optimization algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ansätze for the maximum-cut problem on connected graphs, while focusing on the generated Lie algebras as well as their invariant subspaces. Specifically, we analyze the standard QAOA ansatz as well as the orbit and multiangle ansätze. We are able to fully characterize the Lie algebras of the multiangle ansatz across arbitrary connected graphs, finding that they only fall into one of just six families. Aside from the cycle and path graphs, the Lie dimensions for every graph are exponentially large in the system size, meaning that multiangle ansätze are extremely prone to exhibiting barren plateaus. Then, a similar quasi-graph-independent Lie-algebraic characterization beyond the multiangle ansatz is impeded as the circuit exhibits additional “hidden” symmetries besides those naturally arising from a certain parity-superselection operator and all automorphisms of the considered graph. Disregarding the “hidden” symmetries, we can upper bound the dimensions of the orbit and the standard Lie algebras, and the dimensions of the associated invariant subspaces are determined via explicit character formulas. To finish, we conjecture that (for most graphs) the standard Lie algebras have only components that are either exponential or that grow, at most, polynomially with the system size. This would imply that the QAOA is either prone to barren plateaus or classically simulable. More generally, our work provides a symmetry framework and tools to analyze any desired variational quantum algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Large N algebras and generalized entropy

We construct a Type II ∞ von Neumann algebra that describes the large N physics of single-trace operators in AdS/CFT in the microcanonical ensemble, where there is no need to include perturbative 1/N corrections. Using only the extrapolate dictionary, we show that the entropy of semiclassical states on this algebra is holographically dual to the generalized entropy of the black hole bifurcation surface. From a boundary perspective, this constitutes a derivation of a special case of the QES prescription without any use of Euclidean gravity or replicas; from a purely bulk perspective, it is a derivation of the quantum-corrected Bekenstein-Hawking formula as the entropy of an explicit algebra in the G → 0 limit of Lorentzian effective field theory quantum gravity. In a limit where a black hole is first allowed to equilibrate and then is later potentially re-excited, we show that the generalized second law is a direct consequence of the monotonicity of the entropy of algebras under trace-preserving inclusions. Finally, by considering excitations that are separated by more than a scrambling time we construct a “free product” von Neumann algebra that describes the semiclassical physics of long wormholes supported by shocks. We compute Rényi entropies for this algebra and show that they are equal to a sum over saddles associated to quantum extremal surfaces in the wormhole. Surprisingly, however, the saddles associated to “bulge” quantum extremal surfaces contribute with a negative sign.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Modified multi-dimensional q-deformed Newton oscillators: Algebra, interpolating statistics and thermodynamics

Highlights: • A new quasi-particle algebra is proposed. • The invariance group of the algebra constructed is shown. • The algebra constructed leads to the interpolating statistics. • Anyonic behavior is studied in two dimensions. - Abstract: In this work, we present a new algebraic modelby constructing the modified multi-dimensional q-deformed bosonic and fermionic Newton oscillator algebras. This construction leads effectively to describe interpolating statistics, which can be used to approach the properties of quasi-particle excitations occurring in many-body interacting quantum systems. It is shown that the model algebras are endowed with the SU{sub φ}(d)- and SU{sub θ}(d)-symmetries, where φ and θ are real parameters describing the special phase shifts between two different modes of the models. Particular emphasis is given to the two-dimensional case, which reveals a suitable framework for analyzing anyonic behavior of the models. Furthermore, we discuss the effects of deformation on the general thermodynamical and statistical properties of gas models of these interpolating statistics particles such as the q-deformed statistical distribution function and the equation of state in two and three dimensions. Finally, we concisely point out other possible physical applications of the present deformed (quasi)particle models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

SODAs: sparse optimization for the discovery of differential and algebraic equations

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by time-scale separation, conservation laws and physical constraints. While sparse optimization has revolutionized model development by allowing data-driven discovery of parsimonious models from a library of possible equations, existing approaches for dynamical systems assume DAEs can be reduced to ODEs by eliminating variables before model discovery. This assumption limits the applicability of such methods for DAE systems with unknown constraints and time scales. We introduce sparse optimization for differential-algebraic systems (SODAs), a data-driven method for the identification of DAEs in their explicit form. By discovering the algebraic and dynamic components sequentially without prior identification of the algebraic variables, this approach leads to a sequence of convex optimization problems. It has the advantage of discovering interpretable models that preserve the structure of the underlying physical system. To this end, SODAs improves since SODAs is singular numerical stability when handling high correlations between library terms, caused by near-perfect algebraic relationships, by iteratively refining the conditioning of the candidate library. We demonstrate the performance of our method on biological, mechanical and electrical systems, showcasing its robustness to noise in both simulated time series and real-time experimental data.

DAE↗
DOE OSTI2024

Local Poincaré algebra from quantum chaos

The local two-dimensional Poincaré algebra near the horizon of an eternal AdS black hole, or in proximity to any bifurcate Killing horizon, is generated by the Killing flow and outward null translations on the horizon. In holography, this local Poincaré algebra is reflected as a pair of unitary flows in the boundary Hilbert space whose generators under modular flow grow and decay exponentially with a maximal Lyapunov exponent. This is a universal feature of many geometric vacua of quantum gravity. To explain this universality, we show that a two-dimensional Poincaré algebra emerges in any quantum system that has von Neumann subalgebras associated with half-infinite modular time intervals (modular future and past subalgebras) in a limit analogous to the near-horizon limit. In ergodic theory, quantum dynamical systems with future or past algebras are called quantum K-systems. The surprising statement is that modular K-systems are always maximally chaotic. Interacting quantum systems in the thermodynamic limit and large N theories above the Hawking-Page phase transition are examples of physical theories with future/past subalgebras. We prove that the existence of (modular) future/past von Neumann subalgebras also implies a second law of (modular) thermodynamics and the exponential decay of (modular) correlators. We generalize our results from the modular flow to any dynamical flow with a positive generator and interpret the positivity condition as quantum detailed balance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

von Neumann algebras in JT gravity

We quantize JT gravity with matter on the spatial interval with two asymptotically AdS boundaries. We consider the von Neumann algebra generated by the right Hamiltonian and the gravitationally dressed matter operators on the right boundary. We prove that the commutant of this algebra is the analogously defined left boundary algebra and that both algebras are type II ∞ factors. These algebras provide a precise notion of the entanglement wedge away from the semiclassical limit. We comment on how the factorization problem differs between pure JT gravity and JT gravity with matter.

2D Gravity↗
DOE OSTI2023

A symmetry algebra in double-scaled SYK

The double-scaled limit of the Sachdev-Ye-Kitaev (SYK) model takes the number of fermions and their interaction number to infinity in a coordinated way. In this limit, two entangled copies of the SYK model have a bulk description of sorts known as the “chord Hilbert space”. We analyze a symmetry algebra acting on this Hilbert space, generated by the two Hamiltonians together with a two-sided operator known as the chord number. This algebra is a deformation of the JT gravitational algebra, and it contains a subalgebra that is a deformation of the \mathfrak{sl}_2 𝔰 𝔩 2 near-horizon symmetries. The subalgebra has finite-dimensional unitary representations corresponding to matter moving around in a discrete Einstein-Rosen bridge. In a semiclassical limit the discreteness disappears and the subalgebra simplifies to \mathfrak{sl}_2 𝔰 𝔩 2 , but with a non-standard action on the boundary time coordinate. One can make the action of \mathfrak{sl}_2 𝔰 𝔩 2 algebra more standard at the cost of extending the boundary circle to include some “fake” portions. Such fake portions also accommodate certain subtle states that survive the semi-classical limit, despite oscillating on the scale of discreteness. We discuss applications of this algebra, including sub-maximal chaos, the traversable wormhole protocol, and a two-sided OPE.

97 MATHEMATICS AND COMPUTING↗