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Found 49 papers, 21 papers with code
Efficient Uncertainty Propagation with Guarantees in Wasserstein Distance
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty.
Certified Neural Approximations of Nonlinear Dynamics
Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.
Formal Uncertainty Propagation for Stochastic Dynamical Systems with Additive Noise
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain.
A general partitioning strategy for non-centralized control
Partitioning is a fundamental challenge for non-centralized control of large-scale systems, such as hierarchical, decentralized, distributed, and coalitional strategies.
Memory-dependent abstractions of stochastic systems through the lens of transfer operators
Towards accounting for non-Markovianity, we introduce memory-dependent abstractions for stochastic systems, capturing dynamics with memory effects.
Temporal Logic Control for Nonlinear Stochastic Systems Under Unknown Disturbances
In this paper, we present a novel framework to synthesize robust strategies for discrete-time nonlinear systems with random disturbances that are unknown, against temporal logic specifications.
Scalable control synthesis for stochastic systems via structural IMDP abstractions
We show that such a specific form in the transition probabilities allows one to build compositional abstractions of stochastic systems that, for each state, are only required to store the marginal probability bounds of the original system.
Error Bounds for Physics-Informed Neural Networks in Fokker-Planck PDEs
In this work, we show that physics-informed neural networks (PINNs) can be trained to approximate the solution PDF.
A data-driven approach for safety quantification of non-linear stochastic systems with unknown additive noise distribution
In this paper, we present a novel data-driven approach to quantify safety for non-linear, discrete-time stochastic systems with unknown noise distribution.
Error Bounds For Gaussian Process Regression Under Bounded Support Noise With Applications To Safety Certification
Gaussian Process Regression (GPR) is a powerful and elegant method for learning complex functions from noisy data with a wide range of applications, including in safety-critical domains.
Finite Neural Networks as Mixtures of Gaussian Processes: From Provable Error Bounds to Prior Selection
parameters, with a mixture of Gaussian processes with error bounds on the approximation error.
Data-Driven Strategy Synthesis for Stochastic Systems with Unknown Nonlinear Disturbances
In this paper, we introduce a data-driven framework for synthesis of provably-correct controllers for general nonlinear switched systems under complex specifications.
Data-Driven Permissible Safe Control with Barrier Certificates
This paper introduces a method of identifying a maximal set of safe strategies from data for stochastic systems with unknown dynamics using barrier certificates.
Uncertainty Propagation in Stochastic Systems via Mixture Models with Error Quantification
Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning.
IntervalMDP.jl: Accelerated Value Iteration for Interval Markov Decision Processes
In this paper, we present IntervalMDP. jl, a Julia package for probabilistic analysis of interval Markov Decision Processes (IMDPs).
A Unifying Perspective for Safety of Stochastic Systems: From Barrier Functions to Finite Abstractions
Providing safety guarantees for stochastic dynamical systems is a central problem in various fields, including control theory, machine learning, and robotics.
Probabilistic Reach-Avoid for Bayesian Neural Networks
Such computed lower bounds provide safety certification for the given policy and BNN model.
Formal Abstraction of General Stochastic Systems via Noise Partitioning
We introduce a general procedure for the finite abstraction of nonlinear stochastic systems with non-standard (e. g., non-affine, non-symmetric, non-unimodal) noise distributions for verification purposes.
Promises of Deep Kernel Learning for Control Synthesis
Deep Kernel Learning (DKL) combines the representational power of neural networks with the uncertainty quantification of Gaussian Processes.
Adversarial Robustness Certification for Bayesian Neural Networks
We study the problem of certifying the robustness of Bayesian neural networks (BNNs) to adversarial input perturbations.
BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programming
In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs).
Individual Fairness in Bayesian Neural Networks
We study Individual Fairness (IF) for Bayesian neural networks (BNNs).
Inner approximations of stochastic programs for data-driven stochastic barrier function design
In particular, we show that the stochastic program to synthesize a SBF can be relaxed into a chance-constrained optimisation problem on which scenario approach theory applies.
Efficient Strategy Synthesis for Switched Stochastic Systems with Distributional Uncertainty
First, we construct a finite abstraction of the switched stochastic system as a \emph{robust Markov decision process} (robust MDP) that encompasses both the stochasticity of the system and the uncertainty in the noise distribution.
Interval Markov Decision Processes with Continuous Action-Spaces
Interval Markov Decision Processes (IMDPs) are finite-state uncertain Markov models, where the transition probabilities belong to intervals.
On the Robustness of Bayesian Neural Networks to Adversarial Attacks
Despite significant efforts, both practical and theoretical, training deep learning models robust to adversarial attacks is still an open problem.
Safety Guarantees for Neural Network Dynamic Systems via Stochastic Barrier Functions
A key step in our method is the employment of the recent convex approximation results for NNs to find piece-wise linear bounds, which allow the formulation of the barrier function synthesis problem as a sum-of-squares optimization program.
Safety Certification for Stochastic Systems via Neural Barrier Functions
In this paper, we parameterize a barrier function as a neural network and show that techniques for robust training of neural networks can be successfully employed to find neural barrier functions.
Individual Fairness Guarantees for Neural Networks
We consider the problem of certifying the individual fairness (IF) of feed-forward neural networks (NNs).
Formal Control Synthesis for Stochastic Neural Network Dynamic Models
Neural networks (NNs) are emerging as powerful tools to represent the dynamics of control systems with complicated physics or black-box components.
Formal Analysis of the Sampling Behaviour of Stochastic Event-Triggered Control
Analyzing Event-Triggered Control's (ETC) sampling behaviour is of paramount importance, as it enables formal assessment of its sampling performance and prediction of its sampling patterns.
Formal Verification of Unknown Dynamical Systems via Gaussian Process Regression
In this work, we develop a framework for verifying discrete-time dynamical systems with unmodelled dynamics and noisy measurements against temporal logic specifications from an input-output dataset.
Synergistic Offline-Online Control Synthesis via Local Gaussian Process Regression
The online controller may improve the baseline guarantees since it avoids the discretization error and reduces regression error as new data is collected.
A Language for Modeling And Optimizing Experimental Biological Protocols
We should ideally start from an integrated description of both the model and the steps carried out to test it, to concurrently analyze uncertainties in model parameters, equipment tolerances, and data collection.
Certification of Iterative Predictions in Bayesian Neural Networks
We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models.
Adversarial Robustness Guarantees for Gaussian Processes
Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications.
Strategy Synthesis for Partially-known Switched Stochastic Systems
We present a data-driven framework for strategy synthesis for partially-known switched stochastic systems.
Abstracting the Sampling Behaviour of Stochastic Linear Periodic Event-Triggered Control Systems
Recently, there have been efforts towards understanding the sampling behaviour of event-triggered control (ETC), for obtaining metrics on its sampling performance and predicting its sampling patterns.
Bayesian Inference with Certifiable Adversarial Robustness
We consider adversarial training of deep neural networks through the lens of Bayesian learning, and present a principled framework for adversarial training of Bayesian Neural Networks (BNNs) with certifiable guarantees.
Gradient-Free Adversarial Attacks for Bayesian Neural Networks
In particular, we consider genetic algorithms, surrogate models, as well as zeroth order optimization methods and adapt them to the goal of finding adversarial examples for BNNs.
Assessing Robustness of Text Classification through Maximal Safe Radius Computation
Neural network NLP models are vulnerable to small modifications of the input that maintain the original meaning but result in a different prediction.
Probabilistic Safety for Bayesian Neural Networks
We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations.
Robustness of Bayesian Neural Networks to Gradient-Based Attacks
Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications.
Safety Guarantees for Planning Based on Iterative Gaussian Processes
Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty.
Global Adversarial Robustness Guarantees for Neural Networks
We investigate global adversarial robustness guarantees for machine learning models.
Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Control
Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world.
Adversarial Robustness Guarantees for Classification with Gaussian Processes
We apply our method to investigate the robustness of GPC models on a 2D synthetic dataset, the SPAM dataset and a subset of the MNIST dataset, providing comparisons of different GPC training techniques, and show how our method can be used for interpretability analysis.
Statistical Guarantees for the Robustness of Bayesian Neural Networks
We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two.
Robustness Guarantees for Bayesian Inference with Gaussian Processes
Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems.
