Control Oriented Nonlinear Model Reduction for Distributed Parameter Systems

The development of model reduction techniques for physical systems modeled by partial differential equations (PDEs) has been a very active research area. Large number of states is needed to accurately capture the dynamics of such systems which makes them unsuitable for control design. The order of the system must be reduced prior to control design. In this dissertation, new methods that generalize the popular proper orthogonal decomposition (POD) to nonlinear PDEs are investigated. In particular, cluster based POD algorithms are developed and applied to the one and two dimensional Burgers equations that govern a nonlinear convective ow. Each cluster contains relatively close in distance dynamic behavior within itself, and considerably far with respect to other clusters. Three different clustering schemes in time, space and space-time are proposed. A complete and detailed approach for the Orthogonal Locality Preserving Projections (OLPP) modes computation for the incompressible Navier-Stokes PDE that governs the dynamics of the NACA 0015 airfoil fluid flow is presented. Close snapshots in the full order model are forced to stay close in the reduced order model by defining an optimization problem that preserves local distances. Optimal boundary control laws are derived based on the proposed nonlinear reduced order models, and applied to various distributed parameter systems including: Nonlinear convection, temperature control in energy efficient buildings systems governed by the heat equation, power and voltage control in large electromechanical oscillations in the power grid governed by the wave equation, and ow separation control for fluid flows governed by the Navier-Stokes equations

NodeTrix Planarity Testing with Small Clusters

We study the NodeTrix planarity testing problem for flat clustered graphs when the maximum size of each cluster is bounded by a constant $k$. We consider both the case when the sides of the matrices to which the edges are incident are fixed and the case when they can be chosen arbitrarily. We show that NodeTrix planarity testing with fixed sides can be solved in $O(k^{3k+\frac{3}{2}} \cdot n)$ time for every flat clustered graph that can be reduced to a partial 2-tree by collapsing its clusters into single vertices. In the general case, NodeTrix planarity testing with fixed sides can be solved in $O(n)$ time for $k = 2$, but it is NP-complete for any $k > 2$. NodeTrix planarity testing remains NP-complete also in the free sides model when $k > 4$.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Fast Neural Network Predictions from Constrained Aerodynamics Datasets

Incorporating computational fluid dynamics in the design process of jets, spacecraft, or gas turbine engines is often challenged by the required computational resources and simulation time, which depend on the chosen physics-based computational models and grid resolutions. An ongoing problem in the field is how to simulate these systems faster but with sufficient accuracy. While many approaches involve simplified models of the underlying physics, others are model-free and make predictions based only on existing simulation data. We present a novel model-free approach in which we reformulate the simulation problem to effectively increase the size of constrained pre-computed datasets and introduce a novel neural network architecture (called a cluster network) with an inductive bias well-suited to highly nonlinear computational fluid dynamics solutions. Compared to the state-of-the-art in model-based approximations, we show that our approach is nearly as accurate, an order of magnitude faster, and easier to apply. Furthermore, we show that our method outperforms other model-free approaches

Modulo scheduling with integrated register spilling for clustered VLIW architectures

Clustering is a technique to decentralize the design of future wide issue VLIW cores and enable them to meet the technology constraints in terms of cycle time, area and power dissipation. In a clustered design, registers and functional units are grouped in clusters so that new instructions are needed to move data between them. New aggressive instruction scheduling techniques are required to minimize the negative effect of resource clustering and delays in moving data around. In this paper we present a novel software pipelining technique that performs instruction scheduling with reduced register requirements, register allocation, register spilling and inter-cluster communication in a single step. The algorithm uses limited backtracking to reconsider previously taken decisions. This backtracking provides the algorithm with additional possibilities for obtaining high throughput schedules with low spill code requirements for clustered architectures. We show that the proposed approach outperforms previously proposed techniques and that it is very scalable independently of the number of clusters, the number of communication buses and communication latency. The paper also includes an exploration of some parameters in the design of future clustered VLIW cores.Peer ReviewedPostprint (published version