Applied/ACMS/absS19

ACMS Abstracts: Spring 2019

Jerry Zhu (University of Wisconsin-Madison, CS)

Machine Teaching: Optimal Control of Machine Learning

As machine learning is increasingly adopted in science and engineering, it becomes important to take a higher level view where the machine learner is only one of the agents in a multi-agent system. Other agents may have an incentive to control the learner. As examples, in adversarial machine learning an attacker can poison the training data to manipulate the model the learner learns; in education a teacher can optimize the curriculum to enhance student (modeled as a computational learning algorithm) performance. Machine teaching is optimal control theory applied to machine learning: the plant is the learner, the state is the learned model, and the control is the training data. In this talk I survey the mathematical foundation of machine teaching and the new research frontiers opened up by this confluence of machine learning and control theory.

Abhishek Deshpande (UW-Madison, math)

Switches in chemical and biological networks

Switches are ubiquitous in both chemical and biological circuits. We explore the behaviour of autocatalytic switches in the context of the persistence conjecture. We show that networks without autocatalytic switches are persistent. The notion of a “critical siphon” forms the connecting link between autocatalysis and persistence. The talk will expand upon this connection.

Swtiches are also relevant from a biological perspective. We show that catalytic switches help in reducing retroactivity - the back effect on the upstream system when connected to the downstream system. In addition, for certain catalytic networks like the push-pull motif, high rates of energy consumption are not required to attenuate retroactivity. One can accomplish this by reducing the coupling to the push-pull motif. However, this reduction in coupling is not robust to cross-talk caused by leak reactions.

References: 1) https://arxiv.org/abs/1309.3957 2) https://arxiv.org/abs/1708.01792

Chung-Nan Tzou (UW-Madison, Math)

Fluid Models with Sharp Interfaces - Clouds and Plumes

In this talk, I will discuss two models describing the interaction of fluids across sharp interfaces. The first model is a discontinuous Poisson equation where the interfacial discontinuity arises from phase changes such as the interior and exterior of a cloud. A simple second-order numerical scheme aiming at solving this type of equations is proposed and tested. The second model is a simplified system of ODEs describing the mixing of jets and plumes with the ambient fluid. With the ambient density profile being sharply stratified, we established a criterion for a plume to be trapped underwater or rise to the top surface and also showed that this profile is the optimal mixer. This theory has been applied to the Gulf of Mexico oil spill incident and also compared with the data we collected through hands-on experiments in the fluids lab.

Amy Cochran (UW-Madison, Math and Medical Informatics)

A model of online latent state learning

Researchers are increasingly interested in how humans perform a structured form of learning known as latent-state inferences. Latent state inferences refer to someone's ability to weigh competing hypotheses about one’s environment. Critically, this type of learning can help explain behavior and neural activity important to cognitive neuroscience and psychiatry. In this talk, I will first present a model of latent state learning that uses online, or recursive, updates. I will also discuss open questions related to this topic in hopes of generating discussion. Ultimately, I would like to engage students interested in the emerging area of computational psychiatry, as I will be joining the math department as an assistant professor in the Fall.

Kui Ren (Columbia Applied math and UT-Austin Mathematics)

Uncertainty Characterization in Model-Based Inverse and Imaging Problems

In model-based inverse and imaging problems, it is often the case that only a portion of the relevant physical quantities in the model can be reconstructed/imaged. The rest of the model parameters are assumed to be known. In practice, these parameters are often only known partially (up to a certain accuracy). It is therefore important to characterize the dependence of the inversion/imaging results on the accuracy of these parameters. This is an uncertainty quantification problem that is challenging due to the fact that both the map from the uncertainty parameters (the ones we assumed partially known) to the measured data and the map from the measured data to the quantities to be imaged are difficult to analyze. In this talk, we review some recent computaitonal and mathematical results on such uncertainty characterization problems in nonlinear inverse problems for PDEs.