WGFINNs: Weak formulation-based GENERIC formalism informed neural networks
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Mathematics and Computing↗
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Models of Human-Automation Systems: Initial Analysis of the Boeing 737MAX Design
We describe a formal approach to identifying human factors design vulnerabilities and usability concerns in the context of automated control systems. We present an initial analysis of the design of the B737MAX that has suffered two fatal accidents. We highlight two main design vulnerabilities and one usability concern. Key formal generic properties used to identify these vulnerabilities and usability concerns are defined. These generic properties, and others referenced in the paper, can be applied to the analysis of any human-automation system.
HSI↗
tLaSDI: Thermodynamics-informed latent space dynamics identification
Here we propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.
97 MATHEMATICS AND COMPUTING↗
Thermodynamics-informed latent space dynamics identification
This software showcases a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.
Cheung, Siu Wun↗
The formal verification of generic interpreters
The task assignment 3 of the design and validation of digital flight control systems suitable for fly-by-wire applications is studied. Task 3 is associated with formal verification of embedded systems. In particular, results are presented that provide a methodological approach to microprocessor verification. A hierarchical decomposition strategy for specifying microprocessors is also presented. A theory of generic interpreters is presented that can be used to model microprocessor behavior. The generic interpreter theory abstracts away the details of instruction functionality, leaving a general model of what an interpreter does.
Windley, P.↗
Evanescent operators in one-loop matching computations
Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces — the evanescent operators — can ultimately be removed with a suitable renormalization scheme, resulting in a finite shift of the physical operators. Modern Effective Field Theory matching techniques relying on the method of expansion by regions have to be extended to account for this. After illustrating the importance of these shifts in two specific examples, we compute the finite shifts required to remove all evanescent operators appearing in the one-loop matching of generic ultraviolet theories to the Standard Model Effective Field Theory and elucidate the formalism for generic Effective Field Theory calculations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Reuse of a Formal Model for Requirements Validation
This paper reports experience from how a project engaged in the process of requirements analysis for evolutionary builds can reuse the formally specified design model produced for a similar, earlier project in the same domain. Two levels of reuse are described here. First, a formally specified generic design model was generated on one project to systematically capture the design commonality in a set of software monitors on board a spacecraft. These monitors periodically check for faults and invoke recovery software when needed. The paper summarizes the use of the design model to validate the software design of the various monitors on that first project. Secondly, the paper describes how the formal design model created for the first project was reused on a second, subsequent project. The model was reused to validate the evolutionary requirements for the second project's software monitors, which were being developed in a series of builds. Some mismatches due to the very different architectures on the two projects suggested changes to make the model more generic. In addition, several advantages to the reuse of the first project's formal model on the second project are reported.
Lutz, Robyn R.↗
Reuse of a Formal Model for Requirements Validation
This paper report experience from how a project engaged in the process of requirements analysis for evolutionary builds can reuse the formally specified design model produced for a similar, earlier project in the same domain.
requirements↗
Software for integrated manufacturing systems, part 1
For several years, a broad, unified approach to programming manufacturing cells, factory floors, and other manufacturing systems has been developed. It is based on a blending of distributed Ada, software components, generics and formal models. Among other things the machines and devices which make up the components, and the entire manufacturing cell is viewed as an assembly of software components. The purpose of this project is to reduce cost, increase the reliability and increase the flexibility of manufacturing software. An overview is given of the approach and an experimental generic factory floor controller that was developed using the approach is described. The controller is generic in the sense that it can control any one of a large class of factory floors making an arbitrary mix of parts.
Naylor, A. W.↗
Energetically consistent model reduction for metriplectic systems
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not preserve the metriplectic structure which governs long-term stability of the system. Based on proper orthogonal decomposition, a provably convergent metriplectic reduced-order model is formulated which is guaranteed to maintain the algebraic structure necessary for energy conservation and entropy formation. Further, numerical results on benchmark problems show that the proposed method is remarkably stable, leading to improved accuracy over long time scales at a moderate increase in cost over naive methods.
42 ENGINEERING↗
Quarkonium polarization in medium from open quantum systems and chromomagnetic correlators
Here, by considering the Markovian condition and applying the Wigner transformation upon the diagonal spin components of the quarkonium density matrix with the semiclassical expansion, we systematically derive the Boltzmann transport equation for quarkonia with polarization dependence in the quantum optical limit. Unlike the spin-independent collision terms governed by certain chromoelectric field correlators, new gauge invariant correlators of chromomagnetic fields determine the recombination and dissociation terms with polarization dependence at the order we are working. We also derive a Lindblad equation describing the in-medium transitions between spin-singlet and spin-triplet heavy quark-antiquark pairs in the quantum Brownian motion limit. The Lindblad equation is governed by new transport coefficients defined in terms of the chromomagnetic field correlators. Our formalism is generic and valid for both weakly coupled and strongly coupled quark gluon plasmas. It can be further applied to study spin alignment of vector quarkonia in heavy ion collisions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quarkonium Polarization Kinetic Equation from Open Quantum Systems and Effective Field Theories
Recent measurements of polarization phenomena in relativistic heavy ion collisions have aroused a great interest in understanding dynamical spin evolution of the QCD matter. In particular, the spin alignment signature of J/ψ has been recently observed in Pb-Pb collisions at LHC, which may infer nontrivial spin transport of quarkonia in quark gluon plasmas. Motivated by this, we study the spin-dependent in-medium dynamics of quarkonia by using the potential nonrelativistic QCD (pNRQCD) and the open quantum system framework. By applying the Markovian approximation and Wigner transformation, we systematically derive the Boltzmann transport equation for vector quarkonia with polarization dependence in the quantum optical limit. As opposed to the previous study for the spin-independent case where the collision terms depend on chromoelectric correlators, the new kinetic equation incorporates gauge invariant correlators of chromomagnetic fields that determine the recombination and dissociation terms with polarization dependence at the order we are working in the multipole expansion. In the quantum Brownian motion limit, the Lindblad equation with new transport coefficients defined in terms of the chromomagnetic field correlators have also been derived. Our formalism is generic and valid for both weakly-coupled and strongly-coupled quark gluon plasmas. It may be further applied to study spin alignment of vector quarkonia in heavy ion collisions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Software for integrated manufacturing systems, part 2
Part 1 presented an overview of the unified approach to manufacturing software. The specific characteristics of the approach that allow it to realize the goals of reduced cost, increased reliability and increased flexibility are considered. Why the blending of a components view, distributed languages, generics and formal models is important, why each individual part of this approach is essential, and why each component will typically have each of these parts are examined. An example of a specification for a real material handling system is presented using the approach and compared with the standard interface specification given by the manufacturer. Use of the component in a distributed manufacturing system is then compared with use of the traditional specification with a more traditional approach to designing the system. An overview is also provided of the underlying mechanisms used for implementing distributed manufacturing systems using the unified software/hardware component approach.
Volz, R. A.↗
Incorporating DD π effects and left-hand cuts in lattice QCD studies of the T cc (3875) +
We generalize the relativistic field-theoretic three-particle finite-volume scattering formalism to describe generic DDπ systems in the charm C = 2 sector. This includes the isospin-0 channel, in which the recently discovered doubly-charmed tetraquark T cc (3875) + is expected to manifest as a pole in the DDπ → DDπ scattering amplitude. The formalism presented here can also be applied to lattice QCD settings in which the D * is bound and, in particular, remains valid below the left-hand cut in DD * scattering, thus resolving an issue in previous analyses of lattice-determined finite-volume energies.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A Generic Software Safety Document Generator
Formal certification is based on the idea that a mathematical proof of some property of a piece of software can be regarded as a certificate of correctness which, in principle, can be subjected to external scrutiny. In practice, however, proofs themselves are unlikely to be of much interest to engineers. Nevertheless, it is possible to use the information obtained from a mathematical analysis of software to produce a detailed textual justification of correctness. In this paper, we describe an approach to generating textual explanations from automatically generated proofs of program safety, where the proofs are of compliance with an explicit safety policy that can be varied. Key to this is tracing proof obligations back to the program, and we describe a tool which implements this to certify code auto-generated by AutoBayes and AutoFilter, program synthesis systems under development at the NASA Ames Research Center. Our approach is a step towards combining formal certification with traditional certification methods.
Denney, Ewen↗
Evidence Arguments for Using Formal Methods in Software Certification
We describe a generic approach for automatically integrating the output generated from a formal method/tool into a software safety assurance case, as an evidence argument, by (a) encoding the underlying reasoning as a safety case pattern, and (b) instantiating it using the data produced from the method/tool. We believe this approach not only improves the trustworthiness of the evidence generated from a formal method/tool, by explicitly presenting the reasoning and mechanisms underlying its genesis, but also provides a way to gauge the suitability of the evidence in the context of the wider assurance case. We illustrate our work by application to a real example-an unmanned aircraft system- where we invoke a formal code analysis tool from its autopilot software safety case, automatically transform the verification output into an evidence argument, and then integrate it into the former.
Argumentation↗
Formal proof of the AVM-1 microprocessor using the concept of generic interpreters
A microprocessor designated AVM-1 was designed to demonstrate the use of generic interpreters in verifying hierarchically decomposed microprocessor specifications. This report is intended to document the high-order language (HOL) code verifying AVM-1. The organization of the proof is discussed and some technical details concerning the execution of the proof scripts in HOL are presented. The proof scripts used to verify AVM-1 are also presented.
Windley, P.↗
Implementing the finite-volume three-pion scattering formalism across all non-maximal isospins
We present a numerical exploration of the relativistic-field-theory (RFT) formalism for three pions with all possible values of non-maximal isospin, I πππ = 2, 1 and 0. Using the generic-isospin extension of the RFT formalism [1] and applying our open-source Python library to implement the framework, we predict a range of three-pion energies for illustrative values of the two-to-two scattering amplitudes for various finite-volume irreps also with non-zero total momentum P in the finite-volume frame. The results restrict attention to the case of a vanishing intrinsic three-body interaction so that the spectra can be understood as a baseline. In future lattice QCD calculations, deviations from these values will be translated into evidence for intrinsic three-body effects in the various scattering channels.
hadronic spectroscopy↗