We demonstrate an end-to-end framework to improve the resilience of man-made systems to unforeseen events. The framework is based on a physics-based digital twin model and three modules tasked with real-time fault diagnosis, prognostics and reconfiguration. The fault diagnosis module uses model-based diagnosis algorithms to detect and isolate faults and generates interventions in the system to disambiguate uncertain diagnosis solutions. We scale up the fault diagnosis algorithm to the required real-time performance through the use of parallelization and surrogate models of the physics-based digital twin. The prognostics module tracks fault progression and trains the online degradation models to compute remaining useful life of system components. In addition, we use the degradation models to assess the impact of the fault progression on the operational requirements. The reconfiguration module uses PDDL-based planning endowed with semantic attachments to adjust the system controls to minimize the fault impact on the system operation. We define a resilience metric and use a fuel system example to demonstrate how the metric improves with our framework.

We introduce two block coordinate descent algorithms for solving optimization problems with ordinary differential equations (ODEs) as dynamical constraints. In contrast to prior algorithms, ours do not need to implement sensitivity analysis methods to evaluate loss function gradients. They result from the reformulation of the original problem as an equivalent optimization problem with equality constraints. In our first algorithm we avoid explicitly solving the ODE by integrating the ODE solver as a sequence of implicit constraints. In our second algorithm, we add an ODE solver to reset the estimate of the ODE solution, but no sensitivity analysis method is needed. We test the proposed algorithms on the problem of learning the parameters of the Cucker-Smale model. The algorithms are compared with gradient descent algorithms based on ODE solvers endowed with sensitivity analysis capabilities. We show that the proposed algorithms are at least 4x faster when implemented in Pytorch, and at least 16x faster when implemented in Jax. For large versions of the Cucker-Smale model, the Jax implementation is thousands of times faster. Our algorithms generate more accurate results both on training and test data. In addition, we show how the proposed algorithms scale with the number of optimization variables, and how they can be applied to learning black-box models of dynamical systems. Moreover, we demonstrate how our approach can be combined with approaches based on sensitivity analysis enabled ODE solvers to reduce the training time.

In Model-Based Diagnosis (MBD), we concern ourselves with the health and safety of physical and software systems. Although we often use different knowledge representations and algorithms, some tools like satisfiability (SAT) solvers and temporal logics, are used in both domains. In this paper we introduce Finite Trace Next Logic (FTNL) models of sequential circuits and propose an enhanced algorithm for computing minimal-cardinality diagnoses. Existing state-of-the-art satisfiability algorithms for minimal diagnosis use Sorting Networks (SNs) for constraining the cardinality of the diagnostic candidates. In our approach we exploit Multi-Operand Adders (MOAs). Based on extensive tests with ISCAS-89 circuits, we found that MOAs enable Conjunctive Normal Form (CNF) encodings that are significantly more compact. These encodings lead to 19.7 to 67.6 times fewer variables and 18.4 to 62 times fewer clauses. For converting an FTNL model to CNF, we could achieve a speed-up ranging from 6.2 to 22.2. Using SNs fosters 3.4 to 5.5 times faster on-line satisfiability checking though. This makes MOAs preferable for applications where RAM and off-line time are more limited than on-line CPU time.

We introduce a novel machine learning-based fusion model termed as PI-LSTM (Physics-Infused Long Short-Term Memory Networks) that integrates first principle Physics-Based Models and Long Short-Term Memory (LSTM) network. Our architecture aims at combining equation-based models with data-driven machine learning models to enable accurate predictions of complex dynamic systems. In this hybrid architecture, recurrency aids the temporal memory of the inputs and output of the partial physics model, in a way that facilitates generalization with scarce data sets. We illustrate the application of PI-LSTM on two dynamical systems namely Inverted Pendulum and Tumor Growth. Empirical results on both test problems stand witness to the effectiveness of using physics in guiding machine learning models and the superiority of the outlined hybrid model over purely data-driven models.

In this paper, we investigate the design of optimal state estimators for Markovian jump linear systems. We consider that the state has two components: the first component is finite valued and is denoted as mode, while the second (continuous) component is in a finite dimensional Euclidean space. The continuous state is driven by a zero mean, white and Gaussian process noise. The observation output has two components: the first is the mode and the second is a linear combination of the continuous state observed and zero mean, white Gaussian noise. Both output components are affected by delays, not necessarily equal. Our paradigm is to design optimal estimators for the current state, given the current output observation. We provide a solution to this paradigm by giving a recursive estimator for the continuous state, in the minimum mean square sense, and a finitely parameterized recursive scheme for computing the probability mass function of the current mode conditioned on the observed output. We show that when the mode is observed with a greater delay then the continuous output component, the optimal estimator nonlinear in the observed outputs.