Related papers: Nature's Cost Function: Simulating Physics by Mini…
Light has a fascinating property: it always travels the path that takes the least time between any two points. This is the motivating property behind optical phenomena such as Reflection and Refraction. The unreasonable economic efficiency…
Some problems founds in teaching physics related to curved paths that are unfortunately only described as illustration. A simple way to introduce the path is presented, which can help students to test their concept numerically. The…
We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting…
This article examines a symbolic numerical approach to optimize a vehicle's track for autonomous driving and collision avoidance. The new approach uses the classical cost function definition incorporating the essential aspects of the…
A dual formalism for Lagrange multipliers is developed. The formalism is used to minimize an action function $S(q_2,q_1,T)$ without any dynamical input other than that $S$ is convex. All the key equations of analytical mechanics -- the…
Modern optimal control theory involves adjoining the already known equations of motion of a dynamic system to the objective function using dynamic costates; this is done in order to constrain the optimal control solutions to satisfy the…
The paper considers the problem of constructing program control for an object described by a system with a quasidifferentiable right-hand side. The control aim is to bring the system from a given initial position to a given final state in…
An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
Multi-physics simulations play a crucial role in understanding complex systems. However, their computational demands are often prohibitive due to high dimensionality and complex interactions, such that actual calculations often rely on…
The old problem exists for a driven (time-dependent) quantum oscillator: to differ the true vacuum state from the squeezed one. We suggest finding the true vacuum state by minimization of the functional containing the difference of the…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
We propose a function-learning methodology with a control-theoretical foundation. We parametrise the approximating function as the solution to a control system on a reproducing-kernel Hilbert space, and propose several methods to find the…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
Variational algorithms have particular relevance for near-term quantum computers but require non-trivial parameter optimisations. Here we propose Analytic Descent: Given that the energy landscape must have a certain simple form in the local…
In a world made of atoms, the computer simulation of molecular systems, such as proteins in water, plays an enormous role in science. Software packages that perform these computations have been developed for decades. In molecular…
We focus on autonomously generating robot motion for day to day physical tasks that is expressive of a certain style or emotion. Because we seek generalization across task instances and task types, we propose to capture style via cost…
The calculus of variation and the construction of path integrals is revisited within the framework of non-linear generalized functions. This allows us to make a rigorous analysis of the variation of an action that takes into account the…