no code implementations • 21 Jan 2024 • Akash Harapanahalli, Saber Jafarpour, Samuel Coogan
We present an implementation of interval analysis and mixed monotone interval reachability analysis as function transforms in Python, fully composable with the computational framework JAX.
no code implementations • 17 Sep 2023 • Saber Jafarpour, Samuel Coogan
Interval Markov decision processes are a class of Markov models where the transition probabilities between the states belong to intervals.
1 code implementation • 16 Sep 2023 • Akash Harapanahalli, Saber Jafarpour, Samuel Coogan
We present a framework based on interval analysis and monotone systems theory to certify and search for forward invariant sets in nonlinear systems with neural network controllers.
no code implementations • 27 Jul 2023 • Saber Jafarpour, Akash Harapanahalli, Samuel Coogan
We propose two methods for constructing closed-loop embedding systems, which account for the interactions between the system and the controller in different ways.
no code implementations • 27 Jun 2023 • Akash Harapanahalli, Saber Jafarpour, Samuel Coogan
In this paper, we present a toolbox for interval analysis in numpy, with an application to formal verification of neural network controlled systems.
1 code implementation • 7 Apr 2023 • Akash Harapanahalli, Saber Jafarpour, Samuel Coogan
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances.
3 code implementations • 19 Jan 2023 • Saber Jafarpour, Akash Harapanahalli, Samuel Coogan
This embedding provides a scalable approach for safety analysis of the neural control loop while preserving the nonlinear structure of the system.
no code implementations • 8 Aug 2022 • Saber Jafarpour, Alexander Davydov, Matthew Abate, Francesco Bullo, Samuel Coogan
Third, we use the upper bounds of the Lipschitz constants and the upper bounds of the tight inclusion functions to design two algorithms for the training and robustness verification of implicit neural networks.
1 code implementation • 1 Apr 2022 • Alexander Davydov, Saber Jafarpour, Matthew Abate, Francesco Bullo, Samuel Coogan
We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs).
no code implementations • 10 Jan 2022 • Marco Coraggio, Saber Jafarpour, Francesco Bullo, Mario di Bernardo
Given a flow network with variable suppliers and fixed consumers, the minimax flow problem consists in minimizing the maximum flow between nodes, subject to flow conservation and capacity constraints.
no code implementations • 10 Dec 2021 • Saber Jafarpour, Matthew Abate, Alexander Davydov, Francesco Bullo, Samuel Coogan
First, given an implicit neural network, we introduce a related embedded network and show that, given an $\ell_\infty$-norm box constraint on the input, the embedded network provides an $\ell_\infty$-norm box overapproximation for the output of the given network.
1 code implementation • NeurIPS 2021 • Saber Jafarpour, Alexander Davydov, Anton V. Proskurnikov, Francesco Bullo
Additionally, we design a training problem with the well-posedness condition and the average iteration as constraints and, to achieve robust models, with the input-output Lipschitz constant as a regularizer.
no code implementations • ICLR 2021 • Arlei Lopes da Silva, Furkan Kocayusufoglu, Saber Jafarpour, Francesco Bullo, Ananthram Swami, Ambuj Singh
The flow estimation problem consists of predicting missing edge flows in a network (e. g., traffic, power and water) based on partial observations.
no code implementations • 16 May 2020 • Kevin D. Smith, Saber Jafarpour, Ananthram Swami, Francesco Bullo
Many tasks regarding the monitoring, management, and design of communication networks rely on knowledge of the routing topology.
no code implementations • 27 Mar 2020 • Pedro Cisneros-Velarde, Saber Jafarpour, Francesco Bullo
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis.