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Found 15 papers, 5 papers with code
$\texttt{immrax}$: A Parallelizable and Differentiable Toolbox for Interval Analysis and Mixed Monotone Reachability in JAX
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.
A Contracting Dynamical System Perspective toward Interval Markov Decision Processes
Interval Markov decision processes are a class of Markov models where the transition probabilities between the states belong to intervals.
Forward Invariance in Neural Network Controlled Systems
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.
Efficient Interaction-Aware Interval Analysis of Neural Network Feedback Loops
We propose two methods for constructing closed-loop embedding systems, which account for the interactions between the system and the controller in different ways.
A Toolbox for Fast Interval Arithmetic in numpy with an Application to Formal Verification of Neural Network Controlled Systems
In this paper, we present a toolbox for interval analysis in numpy, with an application to formal verification of neural network controlled systems.
Contraction-Guided Adaptive Partitioning for Reachability Analysis of Neural Network Controlled Systems
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.
Interval Reachability of Nonlinear Dynamical Systems with Neural Network Controllers
This embedding provides a scalable approach for safety analysis of the neural control loop while preserving the nonlinear structure of the system.
Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach
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.
Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks
We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs).
Minimax Flow over Acyclic Networks: Distributed Algorithms and Microgrid Application
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.
Robustness Certificates for Implicit Neural Networks: A Mixed Monotone Contractive Approach
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.
Robust Implicit Networks via Non-Euclidean Contractions
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.
Combining Physics and Machine Learning for Network Flow Estimation
The flow estimation problem consists of predicting missing edge flows in a network (e. g., traffic, power and water) based on partial observations.
Topology Inference with Multivariate Cumulants: The Möbius Inference Algorithm
Many tasks regarding the monitoring, management, and design of communication networks rely on knowledge of the routing topology.
Distributed and time-varying primal-dual dynamics via contraction analysis
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis.
