This lets us identify several changes to both the sampling and training processes, as well as preconditioning of the score networks.

Differential equations describe asystem'sbehavior by specifying its instantaneous dynamics.

This supplementary document is organized as follows. We provide details in terms of the concept of'solution' to an SDE, how we use a finite-differences As illustrated in Figure 1 in the main paper, the concept of a'solution' to an SDE is broader than that of This is what is done in this paper. We can now interpret Eq. (7) through these finite difference The model which we call a'GP-SDE' model in the main paper has appeared in various forms in literature before. It directly resembles a'random' ODE model, where the random field Figure 1 in the main paper, just providing further examples from the test set. For the timing experiments in Sec. 3, we constructed a setup that allowed us to control the approximation error.

Policy tree search is a family of tree search algorithms that use a policy to guide the search. These algorithms provide guarantees on the number of expansions required to solve a given problem that are based on the quality of the policy. While these algorithms have shown promising results, the process in which they are trained requires complete solution trajectories to train the policy. Search trajectories are obtained during a trial-and-error search process. When the training problem instances are hard, learning can be prohibitively costly, especially when starting from a randomly initialized policy. As a result, search samples are wasted in failed attempts to solve these hard instances. This paper introduces a novel method for learning subgoal-based policies for policy tree search algorithms. The subgoals and policies conditioned on subgoals are learned from the trees that the search expands while attempting to solve problems, including the search trees of failed attempts. We empirically show that our policy formulation and training method improve the sample efficiency of learning a policy and heuristic function in this online setting.

Neural Information Processing Systems http://nips.cc/

We study accelerated descent dynamics for constrained convex optimization.

The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through time. The discovery of dynamical systems has been indispensable in engineering, as it allows for the analysis and prediction of complex behaviors for computational modeling, diagnostics, prognostics, and control of engineered systems. Joining recent efforts that harness the power of symbolic regression in this domain, we propose a novel framework for the end-to-end discovery of ordinary differential equations (ODEs), termed Grammar-based ODE Discovery Engine (GODE). The proposed methodology combines formal grammars with dimensionality reduction and stochastic search for efficiently navigating high-dimensional combinatorial spaces. Grammars allow us to seed domain knowledge and structure for both constraining, as well as, exploring the space of candidate expressions. GODE proves to be more sample- and parameter-efficient than state-of-the-art transformer-based models and to discover more accurate and parsimonious ODE expressions than both genetic programming- and other grammar-based methods for more complex inference tasks, such as the discovery of structural dynamics. Thus, we introduce a tool that could play a catalytic role in dynamics discovery tasks, including modeling, system identification, and monitoring tasks.

These derivatives are efficient to compute with Taylor-mode automatic differentiation.

This supplementary document is organized as follows. We provide details in terms of the concept of'solution' to an SDE, how we use a finite-differences As illustrated in Figure 1 in the main paper, the concept of a'solution' to an SDE is broader than that of This is what is done in this paper. We can now interpret Eq. (7) through these finite difference The model which we call a'GP-SDE' model in the main paper has appeared in various forms in literature before. It directly resembles a'random' ODE model, where the random field Figure 1 in the main paper, just providing further examples from the test set. For the timing experiments in Sec. 3, we constructed a setup that allowed us to control the approximation error.