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At least 127 records · Page 7

CRCNS22 Learning Rules in the Hippocampus and their Mapping to Neuromorphic Systems (Final Technical Report)

Large scale biologically-realistic computational models are key to investigating the interplay between structure and function in nervous systems, thus paving the way to new clinical methods and neuro-inspired computing solutions. This project focuses on the hippocampus, in particular the CA3-CA1 regions, due to their role in associative learning and memory, pattern separation and completion, and spatial navigation. Investigations into the neuronal organization and learning rule(s) of this circuit can shed light into how declarative memories are formed, stored, recalled and forgotten and inform computational, experimental and clinical neuroscience work. Our project aims at developing a novel data-driven methodology supported by a broad heterogeneous base of neuroscience experimental knowledge and inspired from advances in computer science and engineering. Specifically, this work will benchmark existing and new learning rules within a full-scale spiking neural network simulation of the CA3-CA1 region. The model will be based on an open-source repository, called the Hippocampome, which contains neuronal morphologies, firing patterns, synapse probabilities, and most other required parameters for all known neuron types in the rodent hippocampal formation. The model will be first trained in a supervised fashion for associative memory tasks using backpropagation through time traditionally used in computer science, enhanced with a new technique called the surrogate gradient method. This optimization method will be used to obtain a global loss minimization, but it is not biologically inspired as it assumes the use of data not locally available to the synapses. However, we propose its use as a benchmarking tool, to compare the training performance of local biologically plausible and hardware-mappable learning rules at scale. New rules or combinations will be proposed and tested as needed, based on the obtained results. Progress in this area will also drive the development of novel hardware-mappable algorithms for continual lifelong learning and categorization of new events from few presented examples. This project goes beyond the existing state-of-the-art by looking at large scale realistic neuronal circuits as networks trainable via global optimization methods such as surrogate gradient descent. The objective function of the brain that supports learning is largely unknown, but it is likely that it operates through local learning rules. Studying network trajectories around local minima as proposed in this work represents a useful strategy for understanding whether a network is training by using a specific (set of) learning rule(s). Starting from a completely untrained network is a challenging test since it is difficult to determine how the learning rule affects the trajectory of the network. This interdisciplinary project will help understand what rule governs learning in these regions or if multiple learning rules are involved. The work will develop a robust methodology to measure if the network is converging to the target solution, oscillating around it, or diverging away.

59 BASIC BIOLOGICAL SCIENCES

Optimal thresholds for the estimation of area rain-rate moments by the threshold method

Optimization of the threshold method, achieved by determination of the threshold that maximizes the correlation between an area-average rain-rate moment and the area coverage of rain rates exceeding the threshold, is demonstrated empirically and theoretically. Empirical results for a sequence of GATE radar snapshots show optimal thresholds of 5 and 27 mm/h for the first and second moments, respectively. Theoretical optimization of the threshold method by the maximum-likelihood approach of Kedem and Pavlopoulos (1991) predicts optimal thresholds near 5 and 26 mm/h for lognormally distributed rain rates with GATE-like parameters. The agreement between theory and observations suggests that the optimal threshold can be understood as arising due to sampling variations, from snapshot to snapshot, of a parent rain-rate distribution. Optimal thresholds for gamma and inverse Gaussian distributions are also derived and compared.

Short, David A.

Optimized Vertex Method and Hybrid Reliability

A method of calculating the fuzzy response of a system is presented. This method, called the Optimized Vertex Method (OVM), is based upon the vertex method but requires considerably fewer function evaluations. The method is demonstrated by calculating the response membership function of strain-energy release rate for a bonded joint with a crack. The possibility of failure of the bonded joint was determined over a range of loads. After completing the possibilistic analysis, the possibilistic (fuzzy) membership functions were transformed to probability density functions and the probability of failure of the bonded joint was calculated. This approach is called a possibility-based hybrid reliability assessment. The possibility and probability of failure are presented and compared to a Monte Carlo Simulation (MCS) of the bonded joint.

Smith, Steven A.

Structural optimization of large structural systems by optimality criteria methods

The fundamental concepts of the optimality criteria method of structural optimization are presented. The effect of the separability properties of the objective and constraint functions on the optimality criteria expressions is emphasized. The single constraint case is treated first, followed by the multiple constraint case with a more complex evaluation of the Lagrange multipliers. Examples illustrate the efficiency of the method.

Berke, Laszlo

A Scalable Interior‐Point Gauss–Newton Method for PDE‐Constrained Optimization With Bound Constraints

Here, we present a scalable approach to solve a class of partial differential equation (PDE)‐constrained optimization problems with bound constraints. This approach utilizes a robust full‐space interior‐point (IP)‐Gauss–Newton optimization method. To cope with the poorly‐conditioned IP‐Gauss–Newton saddle‐point linear systems that need to be solved approximately, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE‐constrained optimization problems. A block Gauss–Seidel preconditioner is proposed for the GMRES‐based solution of the IP‐Gauss–Newton linear systems. It is shown, for a large‐class of PDE‐ and bound‐constrained optimization problems, that the spectrum of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix is asymptotically independent of discretization and is not impacted by the ill‐conditioning that notoriously plagues interior‐point methods. We exploit symmetry of the IP‐Gauss–Newton linear systems and propose a regularization and log‐barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)‐based solution of the equivalent IP‐Gauss–Newton–Schur complement linear systems. The eigenvalues of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log‐barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on two example problems. The numerical solution of these optimization problems is shown to require a discretization independent number of IP‐Gauss–Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill‐conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of the preconditioner, achieved via algebraic multigrid component solvers when applicable, and the aforementioned algorithmic scalability permits a parallel scalable means to compute solutions of a large class of PDE‐ and bound‐constrained problems.

PDE-constrained optimization

Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.

Yamaleev, N. K.

Optimization of Variable Depth Acoustic Liners with Grazing Flow

Acoustic liners, typically used as a noise control treatment in the engine nacelles of conventional aircraft, are being considered for noise treatment in the proprotor ducts of a vertical takeoff and landing aircraft. This work considers a new optimization method to design an acoustic liner with variable depth cavities for broadband and low-frequency attenuation. This method, termed the direct optimization method, minimizes the radiated sound from a duct. In this paper, the new method is compared with an existing indirect method to design multiple variable depth acoustic liners. Acoustic impedances of liners designed using both methods are predicted using a semianalytical impedance model and impedance predictions for two designs are compared to experimental results acquired from grazing flow impedance testing. For the work presented here, liners designed using the indirect approach provide improved attenuation spectra over those designed using the direct approach but potential improvements to the performance of the direction optimization method are discussed.

Proprotor

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.

Aerodynamic optimization studies on advanced architecture computers

The approach to carrying out multi-discipline aerospace design studies in the future, especially in massively parallel computing environments, comprises of choosing (1) suitable solvers to compute solutions to equations characterizing a discipline, and (2) efficient optimization methods. In addition, for aerodynamic optimization problems, (3) smart methodologies must be selected to modify the surface shape. In this research effort, a 'direct' optimization method is implemented on the Cray C-90 to improve aerodynamic design. It is coupled with an existing implicit Navier-Stokes solver, OVERFLOW, to compute flow solutions. The optimization method is chosen such that it can accomodate multi-discipline optimization in future computations. In the work , however, only single discipline aerodynamic optimization will be included.

Chawla, Kalpana

Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing

A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.

Childs, A. G.

Multigrid one shot methods for optimal control problems: Infinite dimensional control

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Arian, Eyal

A novel implementation of method of optimality criterion in synthesizing spacecraft structures with natural frequency constraints

In the design of spacecraft structures, fine tuning the structure to achieve minimum weight with natural frequency constraints is a time consuming process. Here, a novel implementation of the method of optimality criterion (OC) is developed. In this new implementation of OC, the free vibration analysis results are used to compute the eigenvalue sensitivity data required for the formulation. Specifically, the modal elemental strain and kinetic energies are used. Additionally, normalized design parameters are introduced as a second level linking that allows design variables of different values to be linked together. With the use of this novel formulation, synthesis of structures with natural frequency constraint can be carried out manually using modal analysis results. Design examples are presented to illustrate this novel implementation of the optimality criterion method.

Wang, Bo Ping

Aerostructural Level Set Topology Optimization for a Common Research Model Wing

The purpose of this work is to use level set topology optimization to improve the design of a representative wing box structure for the NASA common research model. The objective is to minimize the total compliance of the structure under aerodynamic and body force loading, where the aerodynamic loading is coupled to the structural deformation. A taxi bump case was also considered, where only body force loads were applied. The trim condition that aerodynamic lift must balance the total weight of the aircraft is enforced by allowing the root angle of attack to change. The level set optimization method is implemented on an unstructured three-dimensional grid, so that the method can optimize a wing box with arbitrary geometry. Fast matching and upwind schemes are developed for an unstructured grid, which make the level set method robust and efficient. The adjoint method is used to obtain the coupled shape sensitivities required to perform aerostructural optimization of the wing box structure.

Dunning, Peter D.

Efficient Method for Optimizing Placement of Sensors

A computationally efficient method has been developed to enable optimization of the placement of sensors for the purpose of diagnosis of a complex engineering system (e.g., an aircraft or spacecraft). The method can be used both in (1) designing a sensor system in which the number and positions of sensors are initially not known and must be determined and (2) adding sensors to a pre-existing system to increase the diagnostic capability. The optimal-sensor-placement problem can be summarized as involving the following concepts, issues, and subproblems: a) Degree of Diagnosability - This is a concept for characterizing the set of faults that can be discriminated by use of a given set of sensors. b) Minimal Sensor Set - The idea is one of finding a minimal set of sensors that guarantees a specific degree of diagnosability. c) Minimal-Cost Sensors - In a case in which different sensors are assigned with different costs, it is desired to choose the least costly set of sensors that affords a specific degree of diagnosability.

Fijany, Amir

Asymptotic continuation method for trajectory optimization

A continuation method is applied to a singular perturbation parameter to obtain a new numerical method for computing optimal trajectories. This method allows one to use simply calculated reduced order approximations as starting solutions and continue the perturbation parameter until the optimal full-order solution is obtained. The method does not require the calculation of higher order correction terms nor does it require the perturbation parameter to be small - thus, it has potentially superior convergence properties compared to conventional asymptotic expansions when the perturbation parameter is large. A simple trajectory optimization problem is considered to illustrate the method.

Washburn, R. B., Jr.

New displacement-based methods for optimal truss topology design

Two alternate methods for maximum stiffness truss topology design are presented. The ground structure approach is used, and the problem is formulated in terms of displacements and bar areas. This large, nonconvex optimization problem can be solved by a simultaneous analysis and design approach. Alternatively, an equivalent, unconstrained, and convex problem in the displacements only can be formulated, and this problem can be solved by a nonsmooth, steepest descent algorithm. In both methods, the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix are circumvented. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.

Bendsoe, Martin P.