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1. Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression

   https://doi.org/10.1038/s41467-021-23479-0  

   Reinbold, Patrick_A_K; Kageorge, Logan_M; Schatz, Michael_F; Grigoriev, Roman_O (May 2021, Nature Communications)

   Abstract Machine learning offers an intriguing alternative to first-principle analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws describing simple, low-dimensional systems with low levels of noise. Here we demonstrate that combining a data-driven methodology with some general physical principles enables discovery of a quantitatively accurate model of a non-equilibrium spatially extended system from high-dimensional data that is both noisy and incomplete. We illustrate this using an experimental weakly turbulent fluid flow where only the velocity field is accessible. We also show that this hybrid approach allows reconstruction of the inaccessible variables – the pressure and forcing field driving the flow. 

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2. Machine Learning for Climate Physics and Simulations

   https://doi.org/10.1146/annurev-conmatphys-043024-114758  

   Lai, Ching-Yao; Hassanzadeh, Pedram; Sheshadri, Aditi; Sonnewald, Maike; Ferrari, Raffaele; Balaji, Venkatramani (November 2024, Annual Review of Condensed Matter Physics)

   Abstract We discuss the emerging advances and opportunities at the intersection of machine learning (ML) and climate physics, highlighting the use of ML techniques, including supervised, unsupervised, and equation discovery, to accelerate climate knowledge discoveries and simulations. We delineate two distinct yet complementary aspects: (a) ML for climate physics and (b) ML for climate simulations. Although physics-free ML-based models, such as ML-based weather forecasting, have demonstrated success when data are abundant and stationary, the physics knowledge and interpretability of ML models become crucial in the small-data/nonstationary regime to ensure generalizability. Given the absence of observations, the long-term future climate falls into the small-data regime. Therefore, ML for climate physics holds a critical role in addressing the challenges of ML for climate simulations. We emphasize the need for collaboration among climate physics, ML theory, and numerical analysis to achieve reliable ML-based models for climate applications. 

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3. Data-driven discovery of Green’s functions with human-understandable deep learning

   https://doi.org/10.1038/s41598-022-08745-5  

   Boullé, Nicolas; Earls, Christopher J.; Townsend, Alex (March 2022, Scientific Reports)

   Abstract There is an opportunity for deep learning to revolutionize science and technology by revealing its findings in a human interpretable manner. To do this, we develop a novel data-driven approach for creating a human–machine partnership to accelerate scientific discovery. By collecting physical system responses under excitations drawn from a Gaussian process, we train rational neural networks to learn Green’s functions of hidden linear partial differential equations. These functions reveal human-understandable properties and features, such as linear conservation laws and symmetries, along with shock and singularity locations, boundary effects, and dominant modes. We illustrate the technique on several examples and capture a range of physics, including advection–diffusion, viscous shocks, and Stokes flow in a lid-driven cavity. 

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4. Learning continuous models for continuous physics

   https://doi.org/10.1038/s42005-023-01433-4  

   Krishnapriyan, Aditi S; Queiruga, Alejandro F; Erichson, N Benjamin; Mahoney, Michael W (December 2023, Communications Physics)

   Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications. 

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5. A High-Throughput Microfluidic Cell Sorter Using a Three-Dimensional Coupled Hydrodynamic-Dielectrophoretic Pre-Focusing Module

   https://doi.org/10.3390/mi14101813  

   Aghaamoo, Mohammad; Cardenas-Benitez, Braulio; Lee, Abraham P. (October 2023, Micromachines)

   Beskok, A. (Ed.)

   Dielectrophoresis (DEP) is a powerful tool for label-free sorting of cells, even those with subtle differences in morphological and dielectric properties. Nevertheless, a major limitation is that most existing DEP techniques can efficiently sort cells only at low throughputs (<1 mL h−1). Here, we demonstrate that the integration of a three-dimensional (3D) coupled hydrodynamic-DEP cell pre-focusing module upstream of the main DEP sorting region enables cell sorting with a 10-fold increase in throughput compared to conventional DEP approaches. To better understand the key principles and requirements for high-throughput cell separation, we present a comprehensive theoretical model to study the scaling of hydrodynamic and electrostatic forces on cells at high flow rate regimes. Based on the model, we show that the critical cell-to-electrode distance needs to be ≤10 µm for efficient cell sorting in our proposed microfluidic platform, especially at flow rates ≥ 1 mL h−1. Based on those findings, a computational fluid dynamics model and particle tracking analysis were developed to find optimum operation parameters (e.g., flow rate ratios and electric fields) of the coupled hydrodynamic-DEP 3D focusing module. Using these optimum parameters, we experimentally demonstrate live/dead K562 cell sorting at rates as high as 10 mL h−1 (>150,000 cells min−1) with 90% separation purity, 85% cell recovery, and no negative impact on cell viability. 

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