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DOE OSTI2023

Architecture-Preserving Provable Repair of Deep Neural Networks

Deep neural networks (DNNs) are becoming increasingly important components of software, and are considered the state-of-the-art solution for a number of problems, such as image recognition. However, DNNs are far from infallible, and incorrect behavior of DNNs can have disastrous real-world consequences. This paper addresses the problem of architecture-preserving V-polytope provable repair of DNNs. A V-polytope defines a convex bounded polytope using its vertex representation. V-polytope provable repair guarantees that the repaired DNN satisfies the given specification on the infinite set of points in the given V-polytope. An architecture-preserving repair only modifies the parameters of the DNN, without modifying its architecture. The repair has the flexibility to modify multiple layers of the DNN, and runs in polynomial time. It supports DNNs with activation functions that have some linear pieces, as well as fully-connected, convolutional, pooling and residual layers. To the best our knowledge, this is the first provable repair approach that has all of these features. We implement our approach in a tool called APRNN. Using MNIST, ImageNet, and ACAS Xu DNNs, we show that it has better efficiency, scalability, and generalization compared to PRDNN and REASSURE, prior provable repair methods that are not architecture preserving.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Automation of FARM from Alpha Phase to Beta Phase

Integrated energy systems (IES) combine different energy technologies in synergistic ways to achieve a more secure and economical energy supply. The RAVEN-based HYBRID framework and the RAVEN plugin for grid and capacity optimization (HERON) are used to find the optimal installed capacity and the optimal economical dispatch of each component of the IES, by respecting the limits on the production variables and the corresponding rates of variation (explicit constraints). Besides, there are other process variables whose evolution needs to be bounded to avoid damaging the components (e.g., condensers, heat exchangers, steam generators, etc.) or degrading the process efficiency (e.g., electrolysis in the hydrogen production process). To avoid violating these latter limits (implicit constraints), a proof-of-concept HERON validator based on Feasible Actuator Range Modifier (FARM-Alpha) was developed by Argonne National Laboratory in January 2021. This FARM-Alpha validator calculates the evolution of process variables on whom the implicit constraints are placed, and then provides feedback to HERON dispatcher to adjust the power setpoints of three IES components, i.e., Balance of Plant, Secondary Energy Source, and Thermal Energy Storage, so as to meet both the explicit and implicit constraints. FARM-Alpha was designed to assess the performance of FARM as a HERON validator only, i.e., the list of components and implicit operational constraints were hard-coded within the source code. The lack of flexibility of the corresponding software structure does not allow the deployment in production environment. This report describes the development and the implementation of an enhanced version of the FARM-based validator (FARM-Beta), which ensures more flexibility for the end user in modeling multiple IES configurations and scenarios. Several test cases of the power dispatch problem were then selected to demonstrate the capabilities offered by FARM-beta. The test cases illustrate the efficiency of the closed-loop optimization scheme and the capability to calculate set-point trajectories satisfying both explicit and implicit constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Symmetry Determining Equations of the Rankine-Hugoniot Equations for Variable Velocity Shock Waves

The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.

42 ENGINEERING↗

NASA NTRS1985

An automated methodology development

The design methodology employed in testing the applicability of Ada in large-scale combat simulations is described. Ada was considered as a substitute for FORTRAN to lower life cycle costs and ease the program development efforts. An object-oriented approach was taken, which featured definitions of military targets, the capability of manipulating their condition in real-time, and one-to-one correlation between the object states and real world states. The simulation design process was automated by the problem statement language (PSL)/problem statement analyzer (PSA). The PSL/PSA system accessed the problem data base directly to enhance the code efficiency by, e.g., eliminating non-used subroutines, and provided for automated report generation, besides allowing for functional and interface descriptions. The ways in which the methodology satisfied the responsiveness, reliability, transportability, modifiability, timeliness and efficiency goals are discussed.

Hawley, L. R.↗

NASA NTRS1990

Quadrature imposition of compatibility conditions in Chebyshev methods

This paper handles a problem encountered in the solution by way of Chebyshev spectral collocation discretization of the Poisson equation with homogeneous Neumann boundary conditions. When pseudospectral Chebyshev methodology is utilized to discretize the partial differential equation these integrals have to be approximated by an appropriate quadrature formula. The correct quadrature formula is developed for these problems, taking into account the degree of the polynomials involved. It is shown that this formula leads to a well-conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Gottlieb, D.↗

NASA NTRS1991

A non-iterative method for computing the infimum in H(infinity)-optimization

The authors, as an extension of their earlier work, present a simple noniterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem and is an extension of their earlier work. The problem formulation is general and does not place any restrictions on the direct feedthrough terms between the disturbance input and the measurement output variables. The method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the j-omega axis and also satisfy certain geometric conditions.

Chen, Ben M.↗

NASA NTRS1992

A non-iterative method for computing the infimum in H(infinity)-optimization

This paper presents a simple and non-iterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem, and is an extension of our earlier work. The problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the j-omega axis and also satisfy certain geometric conditions. The computation of the infimum in our method involves solving two well-defined Riccati and two Liapunov equations.

Chen, Ben M.↗

NASA NTRS2003

"Virtual Cockpit Window" for a Windowless Aerospacecraft

A software system processes navigational and sensory information in real time to generate a three-dimensional-appearing image of the external environment for viewing by crewmembers of a windowless aerospacecraft. The design of the particular aerospacecraft (the X-38) is such that the addition of a real transparent cockpit window to the airframe would have resulted in unacceptably large increases in weight and cost. When exerting manual control, an aircrew needs to see terrain, obstructions, and other features around the aircraft in order to land safely. The X-38 is capable of automated landing, but even when this capability is utilized, the crew still needs to view the external environment: From the very beginning of the United States space program, crews have expressed profound dislike for windowless vehicles. The wellbeing of an aircrew is considerably promoted by a three-dimensional view of terrain and obstructions. The present software system was developed to satisfy the need for such a view. In conjunction with a computer and display equipment that weigh less than would a real transparent window, this software system thus provides a virtual cockpit window. The key problem in the development of this software system was to create a realistic three-dimensional perspective view that is updated in real time. The problem was solved by building upon a pre-existing commercial program LandForm C3 that combines the speed of flight-simulator software with the power of geographic-information-system software to generate real-time, three-dimensional-appearing displays of terrain and other features of flight environments. In the development of the present software, the pre-existing program was modified to enable it to utilize real-time information on the position and attitude of the aerospacecraft to generate a view of the external world as it would appear to a person looking out through a window in the aerospacecraft. The development included innovations in realistic horizon-limit modeling, three-dimensional stereographic display, and interfaces for utilization of data from inertial-navigation devices, Global Positioning System receivers, and laser rangefinders.

Abernathy, Michael F.↗

DOE OSTI2021

Real-time Optimal Dispatch of Behind-the-Meter DERs for Secondary Frequency Regulation

Active distribution networks (ADNs) can provide grid services such as peak load shaving, loss reduction, VoltNar control, congestion management, and frequency regulation. The fast response of inverter-based distributed energy resources (DERs) and battery storage systems enables them to provide ramping support and frequency control. This paper proposes a real-time optimization approach for behind-the-meter DERs to participate in the secondary frequency regulation. The proposed approach determines optimal set-points of output power of DERs to respond to requests from system operators (SOs) in realtime to maintain the frequency of the system at the nominal value. To satisfy the real-time requirement for the secondary frequency control, the nonlinear AC power flow model is linearized considering power losses in the system to achieve both high computational speed and acceptable accuracy. The optimization problem is rerun in a closed loop manner until the mismatch between the requested power by the system operators and actual delivered power at the substation reaches an acceptable tolerance. Furthermore, the proposed approach is validated using modified versions of the IEEE 33-bus and IEEE 69-bus distribution systems. Although the contribution of a single distribution system in the frequency regulation may not be significant, stacked and coordinated contributions from several distribution systems can provide frequency regulation and other grid services at scale.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Guaranteeing a Physically Realizable Battery Dispatch Without Charge-Discharge Complementarity Constraints

The non-convex complementarity constraints present a fundamental computational challenge in energy constrained optimization problems. In this work, we present a new, linear, and robust battery optimization formulation that sidesteps the need for battery complementarity constraints and integers and prove analytically that the formulation guarantees that all energy constraints are satisfied which ensures that the optimized battery dispatch is physically realizable. In addition, we bound the worst-case model mismatch and discuss conservativeness. In conclusion, simulation results further illustrate the effectiveness of this approach.

25 ENERGY STORAGE↗

DOE OSTI2023

NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training

This paper presents NSGA-PINN, a multi-objective optimization framework for the effective training of physics-informed neural networks (PINNs). The proposed framework uses the non-dominated sorting genetic algorithm (NSGA-II) to enable traditional stochastic gradient optimization algorithms (e.g., ADAM) to escape local minima effectively. Additionally, the NSGA-II algorithm enables satisfying the initial and boundary conditions encoded into the loss function during physics-informed training precisely. We demonstrate the effectiveness of our framework by applying NSGA-PINN to several ordinary and partial differential equation problems. In particular, we show that the proposed framework can handle challenging inverse problems with noisy data.

Lu, Binghang (ORCID:0009000160016632)↗

NASA NTRS1983

The determination of the elastodynamic fields of an ellipsoidal inhomogeneity

The determination of the elastodynamic fields of an ellipsoidal inhomogeneity is studied in detail via the eigenstrain approach. A complete formulation and a treatment of both types of eigenstrains for equivalence between the inhomogeneity problem and the inclusion problem are given. This approach is shown to be mathematically identical to other approaches such as the direct volume integral formulation. Expanding the eigenstrains and applied strains in the polynomial form in the position vector and satisfying the equivalence conditions at every point, the governing simultaneous algebraic equations for the unknown coefficients in the eigenstrain expansion are derived. The elastodynamic field outside an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the induced displacement field, as well as the differential and total cross sections are formally given in series expansion form for the case of uniformly distributed eigenstrains.

Fu, L. S.↗

NASA NTRS1990

Quadrature imposition of compatibility conditions in Chebyshev methods

Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Gottlieb, D.↗

NASA NTRS1991

Control and applications of cooperating disparate robotic manipulators relevant to nuclear waste management

Remote handling in nuclear waste management requires a robotic system with precise motion as well as a large workspace. The concept of a small arm mounted on the end of a large arm may satisfy such needs. However, the performance of such a serial configuration lacks payload capacity which is a crucial factor for handling a massive object. Also, this configuration induces more flexibility on the structure. To overcome these problems, the topology of bracing the tip of the small arm (not the large arm) and having an end effector in the middle of the chain is proposed in this paper. Also, control of these cooperating disparate manipulators is accomplished in computer simulations. Thus, this robotic system can have the accuracy of the small arm, and at the same time, it can have the payload capacity and large workspace of the large arm.

Lew, Jae Young↗

NASA NTRS2013

JWST Integrated Science Instrument Module Alignment Optimization Tool

During cryogenic vacuum testing of the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM), the global alignment of the ISIM with respect to the designed interface of the JWST optical telescope element (OTE) will be measured through a series of optical characterization tests. These tests will determine the locations and orientations of the JWST science instrument projected focal surfaces and entrance pupils with respect to their corresponding OTE optical interfaces. If any optical performance non-compliances are identified, the ISIM will be adjusted to improve its performance. In order to understand how to manipulate the ISIM's degrees of freedom properly and to prepare for the ISIM flight model testing, a series of optical-mechanical analyses have been completed to develop and identify the best approaches for bringing a non-compliant ISIM element into compliance. In order for JWST to meet its observatory-level optical requirements and ambitious science goals, the ISIM element has to meet approximately 150 separate optical requirements. Successfully achieving many of those optical requirements depends on the proper alignment of the ISIM element with respect to the OTE. To verify that the ISIM element will meet its optical requirements, a series of cryogenic vacuum tests will be conducted with an OTE Simulator (OSIM). An optical Ray Trace and Geometry Model tool was developed to help solve the multi-dimensional alignment problem. The tool allows the user to determine how best to adjust the alignment of the JWST ISIM with respect to the ideal telescope interfaces so that the approximately 150 ISIM optical performance requirements can be satisfied. This capability has not existed previously.

Bos, Brent↗

NASA NTRSDate not supplied

Towards Robust and Accurate Implicit Gradient Methods for Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Discretizations on Tetrahedral Grids

In this paper, we introduce implicit gradient methods as alternatives to conventional least-squares gradient methods for second- and third-order nodal-gradient cell-centered finite-volume discretizations, where solutions are stored at cells but gradients are stored at nodes. Because of the unique configuration of solutions and gradients, implicit gradient systems developed for the node-centered edge-based discretization method can be directly applied once the numerical solutions are interpolated from cells to nodes with sufficient accuracy. The resulting defect-correction solver can be loosely coupled with a flow-equation solver, and at convergence, solutions and gradients that satisfy the corresponding residual equations are obtained. Each iteration is relatively cheap compared with least-squares methods involving hundreds of neighbors. Numerical results are presented for accuracy verification studies and some simple but realistic flow problems.

Computational Fluid Dynamics↗

NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗

NASA NTRS1974

A synthesis theory for the externally excited adaptive system /EEAS/

The externally excited adaptive system (EEAS) is a two-degree-of-freedom feedback system with a nonlinearity which is saturated hard by an external periodic signal. Under certain conditions, the EEAS responds quasi-linearly to command and plant disturbance signals, permitting the development of a quantitative synthesis theory for satisfying system tolerances despite large plant uncertainty. The great advantage of the EEAS is its zero sensitivity to plant gain variations, a property it shares with the self-oscillating adaptive system (SOAS). The EEAS is, however, more flexible than the SOAS in satisfying the quasi-linearity constraints. The essential difference is that in the EEAS the loop transmission bandwidth is not rigorously tied to the 'carrier' signal, as it is in the SOAS. There is a class of problems for which the EEAS is superior to the purely linear system, which in turn is superior to the SOAS. The superiority of the EEAS over the SOAS is especially marked in the case of significant plant disturbances, which generally vitiate a SOAS design.

Horowitz, I. M.↗