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Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We…
When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good…
The principle of optimality is a fundamental aspect of dynamic programming, which states that the optimal solution to a dynamic optimization problem can be found by combining the optimal solutions to its sub-problems. While this principle…
The proposed framework provides a general model of concurrent imperative programming. Programs are modeled as formal languages and concurrency as an interleaving (or shuffle) operator. This yields a simple and elegant algebra of programs.…
Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
In this work we present a theoretical model for differentiable programming. We construct an algebraic language that encapsulates formal semantics of differentiable programs by way of Operational Calculus. The algebraic nature of Operational…
We prove the dynamic programming principle for a class of diffusion processes controlled up to the time of exit from a cylindrical region $[0,T)\times G$. It is assumed that the functional to be maximized is in the Lagrange form with…
Dynamic programming (DP) is a fundamental tool used across many engineering fields. The main goal of DP is to solve Bellman's optimality equations for a given Markov decision process (MDP). Standard methods like policy iteration exploit the…
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…
A core problem in machine learning is to learn expressive latent variables for model prediction on complex data that involves multiple sub-components in a flexible and interpretable fashion. Here, we develop an approach that improves…
We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees. We employ automatic differentiation to obtain direct policy…
Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and…
Differentiable programming is a new programming paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has also been…
We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear…
We present a framework based on Clarke coordinates for spatial displacement-actuated continuum robots with an arbitrary number of joints. This framework consists of three modular components, i.e., a planner, trajectory generator, and…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
We consider a general class of Dynamic Programming (DP) problems with non-separable objective functions. We show that for any problem in this class, there exists an augmented-state DP problem which satisfies the Principle of Optimality and…
Dynamic logic is a powerful approach to reasoning about programs and their executions, obtained by extending classical logic with modalities that can express program executions as formulas. However, the use of dynamic logic in the setting…