Physics-tailored machine learning reveals unexpected physics in dusty plasmas

TL;DR

This work tackles inferring force laws in dusty plasmas, a many-body system with non-reciprocal, wake-mediated interactions, from experimental trajectory data. It introduces physics-constrained machine learning using three neural networks to model interparticle forces, environmental confinement, and drag, trained with a weak-form loss on 3D trajectories to suppress noise. The approach yields accurate force inference with $R^2>0.99$ on accelerations, and enables in situ estimates of particle mass and charge, revealing that the effective screening length $\lambda$ increases with particle size and that $q \propto m^p$ with $p$ between 0.30 and 0.80, deviating from the conventional $q\propto m^{1/3}$. Beyond dusty plasmas, the method demonstrates how physics-informed ML can uncover new dynamics in complex many-body systems.

Abstract

Dusty plasma is a mixture of ions, electrons, and macroscopic charged particles that is commonly found in space and planetary environments. The particles interact through Coulomb forces mediated by the surrounding plasma, and as a result, the effective forces between particles can be non-conservative and non-reciprocal. Machine learning (ML) models are a promising route to learn these complex forces, yet their structure should match the underlying physical constraints to provide useful insight. Here we demonstrate and experimentally validate an ML approach that incorporates physical intuition to infer force laws in a laboratory dusty plasma. Trained on 3D particle trajectories, the model accounts for inherent symmetries, non-identical particles, and learns the effective non-reciprocal forces between particles with exquisite accuracy (R^2>0.99). We validate the model by inferring particle masses in two independent yet consistent ways. The model's accuracy enables precise measurements of particle charge and screening length, discovering large deviations from common theoretical assumptions. Our ability to identify new physics from experimental data demonstrates how ML-powered approaches can guide new routes of scientific discovery in many-body systems. Furthermore, we anticipate our ML approach to be a starting point for inferring laws from dynamics in a wide range of many-body systems, from colloids to living organisms.

Figures (4)

• Figure 1: Overview of experiment and data workflow. ( A) Charged microparticles are levitated in an RF-driven plasma sheath above a flat electrode. Their motion is imaged using a scanning laser sheet coupled to a high-speed camera yu20233d. ( B) Snapshot of particle positions from a single experiment of 15 particles. The grayscale color indicates the $z$-position, and the tails of each particle represent the previous 5 frames. ( C) The focused ion wake (red) is directly below each particle, and contributes a small attractive part of the total force ($F_{ij}$) on particle $i$, so that the overall interaction is nonreciprocal. ( D) The $x$, $y$, and $z$ position of two particles during two seconds. The particles are marked $i$ (blue) and $j$ (red) in panel (C). The quantity $s_i=\langle z_i\rangle$ is used as a size identifier for each particle. ( E) The objective is to infer the horizontal reduced forces on particles using Newton's equation of motion. The schematic of the model, which consists of three neural networks trained concurrently and act as nonlinear approximators to the three terms in the equation (particle interactions -- $f_{ij}$, environmental forces -- $\vec{f}_\text{env}$, and damping from the background gas -- $\gamma_i$). The input color designates the source (particle $i$ or $j$).
• Figure 2: The predicted reduced force ($\vec{f}$, dashed lines) and measured experimental acceleration ($\Ddot {\vec{\rho}}$, solid lines) for 2 particles (red and blue) in the 15 particle system. We note that this is test data, meaning it was not used to train the model. Data is shown for 2 s out of the 4.94 s of test data. The entire experiment was 49.4 s long. ( A) $f_x$ and $\Ddot{\rho}_x$, and ( B) $f_y$ and $\Ddot{\rho}_y$. The two particles are the same particles shown in Fig. \ref{['p1']}.
• Figure 3: Model prediction of interaction and environmental reduced forces for the 15-particle experiment. ( A) The magnitude of the reduced interaction force ($f_{12}$, cyan triangles; $f_{21}$, purple squares) between two similar particles ($s_1 = 0.234$ mm, $s_2 = 0.232$ mm), at $z_1 = 0.15$ mm and $z_2 = 0.30$ mm. The force is plotted versus the horizontal separation $\rho$. The inset shows the interaction at $z_1 = 0.05$ mm and $z_2 = 0.35$ mm. ( B) The model predicts the same two particles' interaction is reciprocal at $z_1 = z_2 = 0.15$ mm. The black solid line is a fit of the average of the two predictions to Eq. \ref{['yukawa']} with $\lambda$ = 0.42 mm. The inset shows the interaction of two different particles ($f_{13}$, brown circles; $f_{31}$, green stars) at $z_1 = z_3 = 0.15$ mm. Here $s_3 = -0.053$ mm, and $f_{31}$ is shifted by a factor of 2.6 (the mass ratio) to collapse the curves. The black solid line is a fit to Eq. \ref{['yukawa']} with $\lambda$ = 0.48 mm. ( C) $f_{12}$ and $f_{21}$ evaluated at $\rho = 0.5$, plotted versus $z = z_1 = z_2$. The sharp rise in the model prediction indicates the boundary between the plasma sheath and bulk plasma (purple). ( D) Environmental reduced force field of particle 1, $\vec{f}_1^{\text{env}}$, at $z_1 = 0.15$ mm. The error bars represent the standard deviation of the prediction from 10 models trained on different sections of the experimental data, as detailed in the SI.
• Figure 4: The inferred measurements of mass, charge, and screening length using Eq. \ref{['yukawa']}, at $z$ = 0.03 mm. ( A) In the 15-particle experiment, the interaction between small particles 1 and 2 ($s_1 = 0.234$ mm, $s_2 = 0.232$ mm, cyan) and between large particles 4 and 5 ($s_4 = -0.150$ mm, $s_5 = -0.161$ mm, gray) have a distinctly different decay with length scale $\lambda$. The solid lines are fits using Eq. \ref{['yukawa']}. Note that a larger $\lambda$ means slower decay. ( B) The mass of all particles inferred from the drag coefficient ($m_\gamma$) versus the mass inferred from the particle interaction ($m_\text{int}$). Different colors represent the 5 different experiments (Table 1). The dashed line is the theoretical value of $m_\gamma = m_\text{int}$. The gray box represents particles with an average diameter of 12.8 $\pm$ 0.32 $\mu$m, corresponding to a mass of $m_0 =$1.65 $\pm$ 0.12 ng, which is necessary for quantifying the mass (see SI for more information). ( C) Particles charge, $q$, versus $m_\text{int}$, both inferred from the fitting procedure using Eq. \ref{['yukawa']}. The dashed lines are power law fits with the fitting power $p$ displayed alongside the lines. In both panels, the two clusters of purple and orange data (indicated by the arrows) each consist of 5 similar particles whose manufacturer-labeled diameters are 9.46 $\pm$ 0.10 $\mu$m (0.66 $\pm$ 0.02 ng) and 8.00 $\pm$ 0.09 $\mu$m (0.40 $\pm$ 0.01 ng), respectively. Inset: the fitting power $p$ versus the plasma pressure $P$. Note that the blue and green data coincide.