Application of Sparse Identification of Nonlinear Dynamics for Physics-Informed Learning

Advances in machine learning and deep neural networks has enabled complex engineering tasks like image recognition, anomaly detection, regression, and multi-objective optimization, to name but a few. The complexity of the algorithm architecture, e.g., the number of hidden layers in a deep neural network, typically grows with the complexity of the problems they are required to solve, leaving little room for interpreting (or explaining) the path that results in a specific solution. This drawback is particularly relevant for autonomous aerospace and aviation systems, where certifications require a complete understanding of the algorithm behavior in all possible scenarios. Including physics knowledge in such data-driven tools may improve the interpretability of the algorithms, thus enhancing model validation against events with low probability but relevant for system certification. Such events include, for example, spacecraft or aircraft sub-system failures, for which data may not be available in the training phase. This paper investigates a recent physics-informed learning algorithm for identification of system dynamics, and shows how the governing equations of a system can be extracted from data using sparse regression. The learned relationships can be utilized as a surrogate model which, unlike typical data-driven surrogate models, relies on the learned underlying dynamics of the system rather than large number of fitting parameters. The work shows that the algorithm can reconstruct the differential equations underlying the observed dynamics using a single trajectory when no uncertainty is involved. However, the training set size must increase when dealing with stochastic systems, e.g., nonlinear dynamics with random initial conditions

A Port Graph Calculus for Autonomic Computing and Invariant Verification

International audienceIn this paper, we first introduce port graphs as graphs with multiple edges and loops, with nodes having explicit connection points, called ports, and edges attaching to ports of nodes. We then define an abstract biochemical calculus that instantiates to a rewrite calculus on these graphs. Rules and strategies are themselves port graphs, i.e. first-class objects of the calculus. As a consequence, they can be rewritten as well, and rules can create new rules, providing a way of modeling adaptive systems. This approach also provides a formal framework to reason about computations and to verify useful properties. We show how structural properties of a modeled system can be expressed as strategies and checked for satisfiability at each step of the computation. This provides a way to ensure invariant properties of a system. This work is a contribution to the formal specification and verification of adaptive systems and to theoretical foundations ofautonomic computing

Compositionality of aspect weaving.

One approach towards adaptivity is aspect-orientation. As- pects enable the systematic addition of code into existing programs. In order to provide safe and at the same time flexible aspects for such adap- tive systems we address the verification of the aspect-oriented language paradigm. This paper first gives an overview of our aspect calculus and summarizes previous results. Then we present a new compositionality lemma prerequisite for so-called run-time weaving. The entire theory and proofs are carried out in the theorem prover Isabelle/HOL

Developing correct, distributed, adaptive software

We illustrate our approach to develop and verify distributed, adaptive software systems. The cornerstone of our framework is the use of choreography languages, which allow us to obtain correctness by construction. Behavioural Design Patterns are also used as abstract tools to design real systems, while techniques based on abstract interpretation and on dynamic verication are integrated in our framework to reduce the complexity of verication