DeepAI AI Chat
Log In Sign Up

Efficient time stepping for numerical integration using reinforcement learning

by   Michael Dellnitz, et al.

Many problems in science and engineering require the efficient numerical approximation of integrals, a particularly important application being the numerical solution of initial value problems for differential equations. For complex systems, an equidistant discretization is often inadvisable, as it either results in prohibitively large errors or computational effort. To this end, adaptive schemes have been developed that rely on error estimators based on Taylor series expansions. While these estimators a) rely on strong smoothness assumptions and b) may still result in erroneous steps for complex systems (and thus require step rejection mechanisms), we here propose a data-driven time stepping scheme based on machine learning, and more specifically on reinforcement learning (RL) and meta-learning. First, one or several (in the case of non-smooth or hybrid systems) base learners are trained using RL. Then, a meta-learner is trained which (depending on the system state) selects the base learner that appears to be optimal for the current situation. Several examples including both smooth and non-smooth problems demonstrate the superior performance of our approach over state-of-the-art numerical schemes. The code is available under


REIN-2: Giving Birth to Prepared Reinforcement Learning Agents Using Reinforcement Learning Agents

Deep Reinforcement Learning (Deep RL) has been in the spotlight for the ...

Personalized Algorithm Generation: A Case Study in Meta-Learning ODE Integrators

We study the meta-learning of numerical algorithms for scientific comput...

Meta-Learning with Self-Improving Momentum Target

The idea of using a separately trained target model (or teacher) to impr...

Self-Adaptive Driving in Nonstationary Environments through Conjectural Online Lookahead Adaptation

Powered by deep representation learning, reinforcement learning (RL) pro...

Closed-Form Analytical Results for Maximum Entropy Reinforcement Learning

We introduce a mapping between Maximum Entropy Reinforcement Learning (M...

A transformation-based approach for solving stiff two-point boundary value problems

A new approach for solving stiff boundary value problems for systems of ...

Towards Data-Driven Offline Simulations for Online Reinforcement Learning

Modern decision-making systems, from robots to web recommendation engine...

Code Repositories