Port-Hamiltonian systems (pHS) allow for a structure-preserving modeling of dynamical systems. Coupling pHS via linear relations between input and output defines an overall pHS, which is structure preserving. However, in multiphysics applications, some subsystems do not allow for a physical pHS description, as (a) this is not available or (b) too expensive. Here, data-driven approaches can be used to deliver a pHS for such subsystems, which can then be coupled to the other subsystems in a structure-preserving way. In this work, we derive a data-driven identification approach for port-Hamiltonian differential algebraic equation (DAE) systems. The approach uses input and state space data to estimate nonlinear effort functions of pH-DAEs. As underlying technique, we us (multi-task) Gaussian processes. This work thereby extends over the current state of the art, in which only port-Hamiltonian ordinary differential equation systems could be identified via Gaussian processes. We apply this approach successfully to two applications from network design and constrained multibody system dynamics, based on pH-DAE system of index one and three, respectively.

Most existing notions of algorithmic fairness are one-shot: they ensure some form of allocative equality at the time of decision making, but do not account for the adverse impact of the algorithmic decisions today on the long-term welfare and prosperity of certain segments of the population. We take a broader perspective on algorithmic fairness. We propose an effort-based measure of fairness and present a data-driven framework for characterizing the long-term impact of algorithmic policies on reshaping the underlying population. Motivated by the psychological literature on social learning and the economic literature on equality of opportunity, we propose a micro-scale model of how individuals respond to decision making algorithms. We employ existing measures of segregation from sociology and economics to quantify the resulting macro-scale population-level change. Importantly, we observe that different models may shift the group-conditional distribution of qualifications in different directions. Our findings raise a number of important questions regarding the formalization of fairness for decision-making models.

We investigate a problem at the intersection of machine learning and security: training-set attacks on machine learners. In such attacks an attacker contaminates the training data so that a specific learning algorithm would produce a model profitable to the attacker. Understanding training-set attacks is important as more intelligent agents (e.g. spam filters and robots) are equipped with learning capability and can potentially be hacked via data they receive from the environment. This paper identifies the optimal training-set attack on a broad family of machine learners. First we show that optimal training-set attack can be formulated as a bilevel optimization problem. Then we show that for machine learners with certain Karush-Kuhn-Tucker conditions we can solve the bilevel problem efficiently using gradient methods on an implicit function. As examples, we demonstrate optimal training-set attacks on Support VectorMachines, logistic regression, and linear regression with extensive experiments. Finally, we discuss potential defenses against such attacks.