# Learning Spatio-Temporal Specifications for Dynamical Systems

arXiv: https://arxiv.org/abs/2112.10714 · HTML: https://mlsanity.com/paper/2112.10714/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 20 Dec 2021.

## Builds on (most cited first, 17 of 17)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Control Synthesis from Linear Temporal Logic Specifications using Model-Free Reinforcement Learning](https://mlsanity.com/paper/1909.07299/) (2019)
- [Specifying User Preferences using Weighted Signal Temporal Logic](https://mlsanity.com/paper/2010.00752/) (2020)
- [Mining Parametric Temporal Logic Properties in Model Based Design for Cyber-Physical Systems](https://mlsanity.com/paper/1512.07956/) (2015)
- [Control from Signal Temporal Logic Specifications with Smooth Cumulative Quantitative Semantics](https://mlsanity.com/paper/1904.11611/) (2019)
- [Deep Convolutional Neural Networks as Generic Feature Extractors](https://mlsanity.com/paper/1710.02286/) (2017)
- [Classification of Time-Series Data Using Boosted Decision Trees](https://mlsanity.com/paper/2110.00581/) (2021)
- [Monitoring Mobile and Spatially Distributed Cyber-Physical Systems](https://mlsanity.com/paper/1904.08847/) (2019)
- [Statistical Verification of Autonomous Systems using Surrogate Models and Conformal Inference](https://mlsanity.com/paper/2004.00279/) (2020)
- [Logic-based Clustering and Learning for Time-Series Data](https://mlsanity.com/paper/1612.07823/) (2016)
- [Graph Temporal Logic Inference for Classification and Identification](https://mlsanity.com/paper/1903.09714/) (2019)
- [Predictive Monitoring with Logic-Calibrated Uncertainty for Cyber-Physical Systems](https://mlsanity.com/paper/2011.00384/) (2020)
- [A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems](https://mlsanity.com/paper/1409.5671/) (2014)
- [Distributed Communication-aware Motion Planning for Multi-agent Systems from STL and SpaTeL Specifications](https://mlsanity.com/paper/1705.10259/) (2017)
- [Neural Network-based Control for Multi-Agent Systems from Spatio-Temporal Specifications](https://mlsanity.com/paper/2104.02737/) (2021)
- [Mining Interpretable Spatio-temporal Logic Properties for Spatially Distributed Systems](https://mlsanity.com/paper/2106.08548/) (2021)

## Built on by (most cited first, 1 of 1)

- [Multi-class Temporal Logic Neural Networks](https://mlsanity.com/paper/2402.12397/) (2024)

## Abstract (arXiv)

Learning dynamical systems properties from data provides important insights that help us understand such systems and mitigate undesired outcomes. In this work, we propose a framework for learning spatio-temporal (ST) properties as formal logic specifications from data. We introduce SVM-STL, an extension of Signal Signal Temporal Logic (STL), capable of specifying spatial and temporal properties of a wide range of dynamical systems that exhibit time-varying spatial patterns. Our framework utilizes machine learning techniques to learn SVM-STL specifications from system executions given by sequences of spatial patterns. We present methods to deal with both labeled and unlabeled data. In addition, given system requirements in the form of SVM-STL specifications, we provide an approach for parameter synthesis to find parameters that maximize the satisfaction of such specifications. Our learning framework and parameter synthesis approach are showcased in an example of a reaction-diffusion system.