Anderson acceleration for geometry optimization and physics simulation

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for interactive applications. Local-global solvers developed in recent years can quickly compute an approximate solution to such problems, making them an attractive choice for applications that prioritize efficiency over accuracy. However, these solvers suffer from lower convergence rate, and may take a long time to compute an accurate result. In this paper, we propose a simple and effective technique to accelerate the convergence of such solvers. By treating each local-global step as a fixed-point iteration, we apply Anderson acceleration, a well-established technique for fixed-point solvers, to speed up the convergence of a local-global solver. To address the stability issue of classical Anderson acceleration, we propose a simple strategy to guarantee the decrease of target energy and ensure its global convergence. In addition, we analyze the connection between Anderson acceleration and quasi-Newton methods, and show that the canonical choice of its mixing parameter is suitable for accelerating local-global solvers. Moreover, our technique is effective beyond classical local-global solvers, and can be applied to iterative methods with a common structure. We evaluate the performance of our technique on a variety of geometry optimization and physics simulation problems. Our approach significantly reduces the number of iterations required to compute an accurate result, with only a slight increase of computational cost per iteration. Its simplicity and effectiveness makes it a promising tool for accelerating existing algorithms as well as designing efficient new algorithms

ASTROD and ASTROD I -- Overview and Progress

In this paper, we present an overview of ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD I mission concepts and studies. The missions employ deep-space laser ranging using drag-free spacecraft to map the gravitational field in the solar-system. The solar-system gravitational field is determined by three factors: the dynamic distribution of matter in the solar system; the dynamic distribution of matter outside the solar system (galactic, cosmological, etc.) and gravitational waves propagating through the solar system. Different relativistic theories of gravity make different predictions of the solar-system gravitational field. Hence, precise measurements of the solar-system gravitational field test all these. The tests and observations include: (i) a precise determination of the relativistic parameters beta and gamma with 3-5 orders of magnitude improvement over previous measurements; (ii) a 1-2 order of magnitude improvement in the measurement of G-dot; (iii) a precise determination of any anomalous, constant acceleration Aa directed towards the Sun; (iv) a measurement of solar angular momentum via the Lense-Thirring effect; (v) the detection of solar g-mode oscillations via their changing gravity field, thus, providing a new eye to see inside the Sun; (vi) precise determination of the planetary orbit elements and masses; (viii) better determination of the orbits and masses of major asteroids; (ix) detection and observation of gravitational waves from massive black holes and galactic binary stars in the frequency range 0.05 mHz to 5 mHz; and (x) exploring background gravitational-waves.Comment: 17 pages, 6 figures, presented to The Third International ASTROD Symposium on Laser Astrodynamics, Space Test of Relativity and Gravitational-Wave Astronomy, Beijing, July 14-16, 2006; International Journal of Modern Physics D, in press (2008

Petawatt laser absorption bounded

The interaction of petawatt ($10^{15}\ \mathrm{W}$) lasers with solid matter forms the basis for advanced scientific applications such as table-top particle accelerators, ultrafast imaging systems and laser fusion. Key metrics for these applications relate to absorption, yet conditions in this regime are so nonlinear that it is often impossible to know the fraction of absorbed light $f$, and even the range of $f$ is unknown. Here using a relativistic Rankine-Hugoniot-like analysis, we show for the first time that $f$ exhibits a theoretical maximum and minimum. These bounds constrain nonlinear absorption mechanisms across the petawatt regime, forbidding high absorption values at low laser power and low absorption values at high laser power. For applications needing to circumvent the absorption bounds, these results will accelerate a shift from solid targets, towards structured and multilayer targets, and lead the development of new materials

Towards a Smart World: Hazard Levels for Monitoring of Autonomous Vehicles’ Swarms

This work explores the creation of quantifiable indices to monitor the safe operations and movement of families of autonomous vehicles (AV) in restricted highway-like environments. Specifically, this work will explore the creation of ad-hoc rules for monitoring lateral and longitudinal movement of multiple AVs based on behavior that mimics swarm and flock movement (or particle swarm motion). This exploratory work is sponsored by the Emerging Leader Seed grant program of the Mineta Transportation Institute and aims at investigating feasibility of adaptation of particle swarm motion to control families of autonomous vehicles. Specifically, it explores how particle swarm approaches can be augmented by setting safety thresholds and fail-safe mechanisms to avoid collisions in off-nominal situations. This concept leverages the integration of the notion of hazard and danger levels (i.e., measures of the “closeness” to a given accident scenario, typically used in robotics) with the concept of safety distance and separation/collision avoidance for ground vehicles. A draft of implementation of four hazard level functions indicates that safety thresholds can be set up to autonomously trigger lateral and longitudinal motion control based on three main rules respectively based on speed, heading, and braking distance to steer the vehicle and maintain separation/avoid collisions in families of autonomous vehicles. The concepts here presented can be used to set up a high-level framework for developing artificial intelligence algorithms that can serve as back-up to standard machine learning approaches for control and steering of autonomous vehicles. Although there are no constraints on the concept’s implementation, it is expected that this work would be most relevant for highly-automated Level 4 and Level 5 vehicles, capable of communicating with each other and in the presence of a monitoring ground control center for the operations of the swarm