Aligning AI-driven discovery with human intuition

TL;DR

This work proposes a new general principle for distilling representations that are naturally more aligned with human intuition, without relying on prior physical knowledge, that can help make human-AI collaboration more fruitful, as well as shed light on how humans make scientific modeling choices.

Abstract

As data-driven modeling of physical dynamical systems becomes more prevalent, a new challenge is emerging: making these models more compatible and aligned with existing human knowledge. AI-driven scientific modeling processes typically begin with identifying hidden state variables, then deriving governing equations, followed by predicting and analyzing future behaviors. The critical initial step of identification of an appropriate set of state variables remains challenging for two reasons. First, finding a compact set of meaningfully predictive variables is mathematically difficult and under-defined. A second reason is that variables found often lack physical significance, and are therefore difficult for human scientists to interpret. We propose a new general principle for distilling representations that are naturally more aligned with human intuition, without relying on prior physical knowledge. We demonstrate our approach on a number of experimental and simulated system where the variables generated by the AI closely resemble those chosen independently by human scientists. We suggest that this principle can help make human-AI collaboration more fruitful, as well as shed light on how humans make scientific modeling choices.

Figures (4)

• Figure 2: Schematic of the TIDE architecture for interpretable state variable discovery. The VAE backbone consists of an encoder $q_\phi$ which maps the input $\mathbf{x}_{i,j}$ to $\mathcal{N}(\bm{\mu}_{i,j}, \bm{\sigma}^2_{i,j})$ and a decoder $p_\theta$ that reconstructs the input from $\mathbf{z}_{i,j} \sim q\phi(\mathbf{z} \mid \mathbf{x}{i,j})$. A dynamics module, $h_\text{dyn}$, is integrated to predict the next latent representation $\hat{\mathbf{z}}_{i,j+1} = h_\text{dyn}(\bm{\mu}_{i,j})$ by maximizing the likelihood. The overall training objective is a weighted combination of the ELBO $\mathcal{L}_\text{ELBO}$, dynamics loss $\mathcal{L}_\text{dyn}$, and time-derivative regularization $\mathcal{L}_\text{reg}$.
• Figure 3: Grid showing the nine evaluation video datasets.
• Figure 4: Visual depiction of state variables for the single pendulum \ref{['fig:single-pendulum-variables']} and double pendulum \ref{['fig:double-pendulum-variables']} over a single video. Human variables are represented with solid lines, while model variables are shown with dashed lines. TIDE learns smoother variables that more closely resemble the angle and angular velocity compared to the baseline. We also depict the symbolic regression fit for the first latent variable in a solid black line. The analytical expressions are provided in Equations \ref{['eq:single-pendulum-formula']} and \ref{['eq:double-pendulum-formula']}.
• Figure 5: Phase space of the model variables on the single pendulum dataset, colored by the angle $\theta$ and angular velocity $\omega$. TIDE (top) generates a continuous latent space, a result of the time-derivative regularization. In contrast, the baseline (bottom) shows discontinuous transitions between consecutive states, which is less aligned with physical intuition.