Flood mapping on Earth imagery is crucial for disaster management, but its efficacy is hampered by the lack of high-quality training labels. Given high-resolution Earth imagery with coarse and noisy training labels, a base deep neural network model, and a spatial knowledge base with label constraints, our problem is to infer the true high-resolution labels while training neural network parameters. Traditional methods are largely based on specific physical properties and thus fall short of capturing the rich domain constraints expressed by symbolic logic. Neural-symbolic models can capture rich domain knowledge, but existing methods do not address the unique spatial challenges inherent in flood mapping on high-resolution imagery. To fill this gap, we propose a spatial-logic-aware weakly supervised learning framework. Our framework integrates symbolic spatial logic inference into probabilistic learning in a weakly supervised setting. To reduce the time costs of logic inference on vast high-resolution pixels, we propose a multi-resolution spatial reasoning algorithm to infer true labels while training neural network parameters. Evaluations of real-world flood datasets show that our model outperforms several baselines in prediction accuracy. The code is available at https://github.com/spatialdatasciencegroup/SLWSL.

Foundation models such as ChatGPT are poised to transform society by providing general intelligence for problem-solving in healthcare, education, and law. They are also expected to make dramatic impacts in the way of AI solving spatiotemporal tasks in the physical world, such as smart manufacturing, intelligent transportation, and Earth system modeling. However, one major handicap is that existing foundation models do not understand the spatiotemporal knowledge of the physical world, leading to unexpected model behaviors and significant safety risks. This paper discusses emerging opportunities and unique challenges in integrating foundation models with physical components for solving spatiotemporal tasks. We also identify several new research directions to enhance the safety of such integrated models by spatiotemporal-knowledge-guided in-context-learning, verification, safety alignment, and the development of physics-informed geo-foundation models, as well as new benchmarking datasets and evaluation metrics.

Deep learning for Earth imagery plays an increasingly important role in geoscience applications such as agriculture, ecology, and natural disaster management. Still, progress is often hindered by the limited training labels. Given Earth imagery with limited training labels, a base deep neural network model, and a spatial knowledge base with label constraints, our problem is to infer the full labels while training the neural network. The problem is challenging due to the sparse and noisy input labels, spatial uncertainty within the label inference process, and high computational costs associated with a large number of sample locations. Existing works on neuro-symbolic models focus on integrating symbolic logic into neural networks (e.g., loss function, model architecture, and training label augmentation), but these methods do not fully address the challenges of spatial data (e.g., spatial uncertainty, the trade-off between spatial granularity and computational costs). To bridge this gap, we propose a novel Spatial Knowledge-Infused Hierarchical Learning (SKI-HL) framework that iteratively infers sample labels within a multi-resolution hierarchy. Our framework consists of a module to selectively infer labels in different resolutions based on spatial uncertainty and a module to train neural network parameters with uncertainty-aware multi-instance learning. Extensive experiments on real-world flood mapping datasets show that the proposed model outperforms several baseline methods. The code is available at https://github.com/ZelinXu2000/SKI-HL.

Experiments with computer processors must account for the inherent variability in executions. Prior work has shown that real systems exhibit variability, and random effects must be injected into simulators to account for it. Thus, we can run multiple executions of a given benchmark and generate a distribution of results. Prior work uses standard statistical techniques that are not suitable. While the result distributions may take any forms that are unknown a priori, many works naively assume they are Gaussian, which can be far from the truth. To allow rigorous evaluation for arbitrary result distributions, we introduce statistical model checking (SMC) to the world of computer architecture. SMC is a statistical technique that is used in research communities that depend heavily on statistical guarantees. SMC provides a rigorous mathematical methodology that employs experimental sampling for probabilistic evaluation of properties of interest, such that one can determine with a desired confidence whether a property (e.g., System X is 1.1x faster than System Y) is true or not. SMC alone is not enough for computer architects to draw conclusions based on their data. We create an end-to-end framework called SMC for Processor Analysis (SPA) which utilizes SMC techniques to provide insightful conclusions given experimental data.

Hyperproperties have shown to be a powerful tool for expressing and reasoning about information-flow security policies. In this paper, we investigate the problem of statistical model checking (SMC) for hyperproperties. Unlike exhaustive model checking, SMC works based on drawing samples from the system at hand and evaluate the specification with statistical confidence. The main benefit of applying SMC over exhaustive techniques is its efficiency and scalability. To reason about probabilistic hyperproperties, we first propose the temporal logic HyperPCTL* that extends PCTL* and HyperPCTL. We show that HyperPCTL* can express important probabilistic information-flow security policies that cannot be expressed with HyperPCTL. Then, we introduce SMC algorithms for verifying HyperPCTL* formulas on discrete-time Markov chains, based on sequential probability ratio tests (SPRT) with a new notion of multidimensional indifference region. Our SMC algorithms can handle both non-nested and nested probability operators for any desired significance level. To show the effectiveness of our technique, we evaluate our SMC algorithms on four case studies focused on information security: timing side-channel vulnerability in encryption, probabilistic anonymity in dining cryptographers, probabilistic noninterference of parallel programs, and the performance of a randomized cache replacement policy that acts as a countermeasure against cache flush attacks.

We consider the problem of security-aware planning in an unknown stochastic environment, in the presence of attacks on control signals (i.e., actuators) of the robot. We model the attacker as an agent who has the full knowledge of the controller as well as the employed intrusion-detection system and who wants to prevent the controller from performing tasks while staying stealthy. We formulate the problem as a stochastic game between the attacker and the controller and present an approach to express the objective of such an agent and the controller as a combined linear temporal logic (LTL) formula. We then show that the planning problem, described formally as the problem of satisfying an LTL formula in a stochastic game, can be solved via model-free reinforcement learning when the environment is completely unknown. Finally, we illustrate and evaluate our methods on two robotic planning case studies.

We study the problem of synthesizing control strategies for Linear Temporal Logic (LTL) objectives in unknown environments. We model this problem as a turn-based zero-sum stochastic game between the controller and the environment, where the transition probabilities and the model topology are fully unknown. The winning condition for the controller in this game is the satisfaction of the given LTL specification, which can be captured by the acceptance condition of a deterministic Rabin automaton (DRA) directly derived from the LTL specification. We introduce a model-free reinforcement learning (RL) methodology to find a strategy that maximizes the probability of satisfying a given LTL specification when the Rabin condition of the derived DRA has a single accepting pair. We then generalize this approach to LTL formulas for which the Rabin condition has a larger number of accepting pairs, providing a lower bound on the satisfaction probability. Finally, we illustrate applicability of our RL method on two motion planning case studies.

We present a scalable methodology to verify stochastic hybrid systems for inequality linear temporal logic (iLTL) or inequality metric interval temporal logic (iMITL). Using the Mori–Zwanzig reduction method, we construct a finite-state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain is approximately equivalent to the original system in a distributional sense. Approximate equivalence of the stochastic hybrid system and its Markov chain reduction means that analyzing the Markov chain with respect to a suitably strengthened property allows us to conclude whether the original stochastic hybrid system meets its temporal logic specifications. Based on this, we propose the first statistical model checking algorithms to verify stochastic hybrid systems against correctness properties, expressed in iLTL or iMITL. The scalability of the proposed algorithms is demonstrated by a case study.

is a statistical model checker that uses antithetic and stratified sampling techniques to reduce the number of samples and, hence, the amount of time required before making a decision. The tool is capable of statistically verifying any black-box probabilistic system that can simulate, against probabilistic bounds on any property that can evaluate over individual executions of the system. We have evaluated our tool on many examples and compared it with both symbolic and statistical algorithms. When the number of strata is large, our algorithms reduced the number of samples more than 3 times on average. Furthermore, being a statistical model checker makes able to verify models that are well beyond the reach of current symbolic model checkers. On large systems (up to $$10^{14}$$ states) was able to check 100% of benchmark systems, compared to existing symbolic methods in , which only succeeded on 13% of systems. The tool, installation instructions, benchmarks, and scripts for running the benchmarks are all available online as open source.

The use of Neural Network (NN)-based controllers has attracted significant attention in recent years. Yet, due to the complexity and non-linearity of such NN-based cyber-physical systems (CPS), existing verification techniques that employ exhaustive state-space search, face significant scalability challenges; this effectively limits their use for analysis of real-world CPS. In this work, we focus on the use of Statistical Model Checking (SMC) for verifying complex NN-controlled CPS. Using an SMC approach based on Clopper-Pearson confidence levels, we verify from samples specifications that are captured by Signal Temporal Logic (STL) formulas. Specifically, we consider three CPS benchmarks with varying levels of plant and controller complexity, as well as the type of considered STL properties - reachability property for a mountain car, safety property for a bipedal robot, and control performance of the closed-loop magnet levitation system. On these benchmarks, we show that SMC methods can be successfully used to provide high-assurance for learning-based CPS.

There is a growing interest on formal methods-based robotic planning for temporal logic objectives. In this work, we extend the scope of existing synthesis methods to hyper-temporal logics. We are motivated by the fact that important planning objectives, such as optimality, robustness, and privacy, (maybe implicitly) involve the interrelation between multiple paths. Such objectives are thus hyperproperties, and cannot be expressed with usual temporal logics like the linear temporal logic (LTL). We show that such hyperproperties can be expressed by HyperLTL, an extension of LTL to multiple paths. To handle the complexity of planning with HyperLTL specifications, we introduce a symbolic approach for synthesizing planning strategies on discrete transition systems. Our planning method is evaluated on several case studies.

We present a reinforcement learning (RL) framework to synthesize a control policy from a given linear temporal logic (LTL) specification in an unknown stochastic environment that can be modeled as a Markov Decision Process (MDP). Specifically, we learn a policy that maximizes the probability of satisfying the LTL formula without learning the transition probabilities. We introduce a novel rewarding and path-dependent discounting mechanism based on the LTL formula such that (i) an optimal policy maximizing the total discounted reward effectively maximizes the probabilities of satisfying LTL objectives, and (ii) a model-free RL algorithm using these rewards and discount factors is guaranteed to converge to such policy. Finally, we illustrate the applicability of our RL-based synthesis approach on two motion planning case studies.

Stochastic multiplayer games (SMGs) have gained attention in the field of strategy synthesis for multi-agent reactive systems. However, standard SMGs are limited to modeling systems where all agents have full knowledge of the state of the game. In this paper, we introduce delayed-action games (DAGs) formalism that simulates hidden-information games (HIGs) as SMGs, where hidden information is captured by delaying a player’s actions. The elimination of private variables enables the usage of SMG off-the-shelf model checkers to implement HIGs. Furthermore, we demonstrate how a DAG can be decomposed into subgames that can be independently explored, utilizing parallel computation to reduce the model checking time, while alleviating the state space explosion problem that SMGs are notorious for. In addition, we propose a DAG-based framework for strategy synthesis and analysis. Finally, we demonstrate applicability of the DAG-based synthesis framework on a case study of a human-on-the-loop unmanned-aerial vehicle system under stealthy attacks, where the proposed framework is used to formally model, analyze and synthesize security-aware strategies for the system.

Many important properties of cyber-physical systems (CPS) are defined upon the relationship between multiple executions simultaneously in continuous time. Examples include probabilistic fairness and sensitivity to modeling errors (i.e., parameters changes) for real-valued signals. These requirements can only be specified by hyperproperties . In this article, we focus on verifying probabilistic hyperproperties for CPS. To cover a wide range of modeling formalisms, we first propose a general model of probabilistic uncertain systems (PUSs) that unify commonly studied CPS models such as continuous-time Markov chains (CTMCs) and probabilistically parametrized Hybrid I/O Automata (P 2 HIOA). To formally specify hyperproperties, we propose a new temporal logic, hyper probabilistic signal temporal logic (HyperPSTL) that serves as a hyper and probabilistic version of the conventional signal temporal logic (STL). Considering the complexity of real-world systems that can be captured as PUSs, we adopt a statistical model checking (SMC) approach for their verification. We develop a new SMC technique based on the direct computation of significance levels of statistical assertions for HyperPSTL specifications, which requires no a priori knowledge on the indifference margin. Then, we introduce SMC algorithms for HyperPSTL specifications on the joint probabilistic distribution of multiple paths, as well as specifications with nested probabilistic operators quantifying different paths, which cannot be handled by existing SMC algorithms. Finally, we show the effectiveness of our SMC algorithms on CPS benchmarks with varying levels of complexity, including the Toyota Powertrain Control System.

The Toyota Powertrain Control Verification Benchmark has been recently proposed as challenge problems that capture features of realistic automotive designs. In this paper we statistically verify the most complicated of the powertrain control models proposed, that includes features like delayed differential and difference equations, look-up tables, and highly non-linear dynamics, by simulating the C++ code generated from the SimulinkTM model of the design. Our results show that for at least 98% of the possible initial operating conditions the desired properties hold. These are the first verification results for this model, statistical or otherwise.

Modeling, analyzing and verifying real physical systems has long been a challenging task since the state space of the systems is usually infinite and the dynamics of the systems is generally nonlinear and stochastic. In this work, we employ an extension of linear temporal logic (LTL) to describe the behavior of discrete-time nonlinear stochastic systems; this extension is so-called linear inequality LTL (iLTL) which allows for atomic propositions that are linear inequalities on state spaces. To statistically verify iLTL formulas on the systems, we first reformulate discrete-time nonlinear stochastic dynamical systems into Markov processes on their continuous state spaces and then reduce them to discrete-time Markov chains (DTMC) using set-oriented methods. Furthermore, a statistical verification algorithm is proposed to verify iLTL formulas on the reduced systems. The correctness of this statistical verification algorithm is checked both by theoretical analysis and the simulation of a fluid problem. We will show in the successive work that the framework extends to hybrid systems, which is a significant motivation for the approach taken.