Ethan Lew

Kamel Lahouel, Michael Wells, Victor Rielly et al.

Learning nonparametric systems of Ordinary Differential Equations (ODEs) dot x = f(t,x) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator and provide experimental comparisons with the state-of-the-art.

Victor Rielly, Kamel Lahouel, Ethan Lew et al.

Learning a nonparametric system of ordinary differential equations from trajectories in a $d$-dimensional state space requires learning $d$ functions of $d$ variables. Explicit formulations often scale quadratically in $d$ unless additional knowledge about system properties, such as sparsity and symmetries, is available. In this work, we propose a linear approach, the multivariate occupation kernel method (MOCK), using the implicit formulation provided by vector-valued reproducing kernel Hilbert spaces. The solution for the vector field relies on multivariate occupation kernel functions associated with the trajectories and scales linearly with the dimension of the state space. We validate through experiments on a variety of simulated and real datasets ranging from 2 to 1024 dimensions. MOCK outperforms all other comparators on 3 of the 9 datasets on full trajectory prediction and 4 out of the 9 datasets on next-point prediction.

Sandeep Neema, Susmit Jha, Adam Nagel et al.

We discuss the challenges and propose a framework for evaluating engineering artificial general intelligence (eAGI) agents. We consider eAGI as a specialization of artificial general intelligence (AGI), deemed capable of addressing a broad range of problems in the engineering of physical systems and associated controllers. We exclude software engineering for a tractable scoping of eAGI and expect dedicated software engineering AI agents to address the software implementation challenges. Similar to human engineers, eAGI agents should possess a unique blend of background knowledge (recall and retrieve) of facts and methods, demonstrate familiarity with tools and processes, exhibit deep understanding of industrial components and well-known design families, and be able to engage in creative problem solving (analyze and synthesize), transferring ideas acquired in one context to another. Given this broad mandate, evaluating and qualifying the performance of eAGI agents is a challenge in itself and, arguably, a critical enabler to developing eAGI agents. In this paper, we address this challenge by proposing an extensible evaluation framework that specializes and grounds Bloom's taxonomy - a framework for evaluating human learning that has also been recently used for evaluating LLMs - in an engineering design context. Our proposed framework advances the state of the art in benchmarking and evaluation of AI agents in terms of the following: (a) developing a rich taxonomy of evaluation questions spanning from methodological knowledge to real-world design problems; (b) motivating a pluggable evaluation framework that can evaluate not only textual responses but also evaluate structured design artifacts such as CAD models and SysML models; and (c) outlining an automatable procedure to customize the evaluation benchmark to different engineering contexts.