Related papers: Expressive Symbolic Regression for Interpretable M…

Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human experts. In particular,…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Time series models with recurrent neural networks (RNNs) can have high accuracy but are unfortunately difficult to interpret as a result of feature-interactions, temporal-interactions, and non-linear transformations. Interpretability is…

Deep neural networks based on layer-stacking architectures have historically suffered from poor inherent interpretability. Meanwhile, symbolic probabilistic models function with clear interpretability, but how to combine them with neural…

We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g.…

As power systems evolve with the increasing integration of renewable energy sources and smart grid technologies, there is a growing demand for flexible and scalable modeling approaches capable of capturing the complex dynamics of modern…

Physics-informed Neural Networks (PINNs) have been widely used to obtain accurate neural surrogates for a system of Partial Differential Equations (PDE). One of the major limitations of PINNs is that the neural solutions are challenging to…

Learning identifiable representations and models from low-level observations is helpful for an intelligent spacecraft to complete downstream tasks reliably. For temporal observations, to ensure that the data generating process is provably…

We explore the promising performance of a transformer model in predicting outputs of parametric dynamical systems with external time-varying input signals. The outputs of such systems vary not only with physical parameters but also with…

Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…

Symbolic regression (SR), the automated discovery of mathematical expressions from data, is a cornerstone of scientific inquiry. However, it is often hindered by the combinatorial explosion of the search space and a tendency to overfit.…

Deep learning has made significant advances in creating efficient representations of time series data by automatically identifying complex patterns. However, these approaches lack interpretability, as the time series is transformed into a…

Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…

This work presents a dual-agent \ac{llm}-based reasoning framework for automated planar mechanism synthesis that tightly couples linguistic specification with symbolic representation and simulation. From a natural-language task description,…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…

Explaining the outcome of deep learning decisions based on affect is challenging but necessary if we expect social companion robots to interact with users on an emotional level. In this paper, we present a commonsense approach that utilizes…

What types of numeric representations emerge in neural systems, and what would a satisfying answer to this question look like? In this work, we interpret Neural Network (NN) solutions to sequence based number tasks using a variety of…

In this paper, we derive closed-form expressions for implicit controlled invariant sets for discrete-time controllable linear systems with measurable disturbances. In particular, a disturbance-reactive (or disturbance feedback) controller…

How can we find interpretable, domain-appropriate models of natural phenomena given some complex, raw data such as images? Can we use such models to derive scientific insight from the data? In this paper, we propose some methods for…

High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most…