Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session M09: Predicting Nonlinear and Complex Systems with Machine Learning IFocus Recordings Available
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Sponsoring Units: GSNP DSOFT DCOMP Chair: Ying-Cheng Lai, Arizona State University Room: McCormick Place W-180 |
Wednesday, March 16, 2022 8:00AM - 8:12AM |
M09.00001: A framework for seismic risk policy design and the assessment of avalanche-like event prediction in knitted fabric. Adèle Douin, Frédéric Lechenault, Jean-Phillipe Bruneton
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Wednesday, March 16, 2022 8:12AM - 8:24AM |
M09.00002: Can graph neural network infer knot invariants? Changyeob Baek, Christopher H Rycroft The intriguing fact of physical knots is that their knot topology, not their specific shape, dictates their physical behavior. This phenomenon can be commonly found in many physical knots, such as entanglements of DNA and polymer chains and those in climbing ropes and shoelaces. It is therefore crucial to identify the topological properties of knots. In this talk, we use a data-driven approach to predict the topologically invariant properties of knots from their centerline conformation. By simulating the random diffusion of strings, we generate multiple groups of knots associated with different knot topologies. Each group contains knots of distinct shapes yet topologically equivalent conformations. Using a graph neural network, we first perform a classification task on the groups of knots and achieve high classification accuracy. Then, we train the neural net to predict the ropelength (which is a scalar-valued knot invariant) of knots and find that the neural network is capable of making the inference of the ropelength of knots which the neural net has not previously seen. Finally, we extend our approach to multi-filament knots, demonstrating that the data-driven approach may be generalized to characterizing physical systems consisting of multiple filaments. |
Wednesday, March 16, 2022 8:24AM - 8:36AM |
M09.00003: Building Deep Learning Architectures for Physics, Chemistry, and Biology with Geometric Algebra Matthew P Spellings Designing deep learning architectures which respect the structure underlying problems of interest can both improve the data efficiency of model training and impose symmetries that are vital for many applications. For physical problems in real space, we would often like to formulate machine learning models which incorporate not only geometric information, but also point-level signals such as the identity of coarse-grained beads, atoms, or protein residues. In this talk, we build permutation- and rotation-equivariant neural network layers for learning on point clouds using geometric algebra and attention mechanisms. We demonstrate the flexibility of these architectures by solving example problems spanning domains from basic physics to biology. |
Wednesday, March 16, 2022 8:36AM - 8:48AM |
M09.00004: Optimal control of quantum thermal machines using machine learning Ilia Khait, Juan Carrasquilla, Dvira Segal We develop a deep learning (DL) framework assisted by differentiable programming for discovery of optimal quantum control protocols under hard constraints. To that end, we use neural network representations to our protocols, whose learning process is done with exact gradients. We find high quality solutions to the optimization problem of finite-time thermodynamical process in a quantum thermal machine. Using this DL algorithm, we show that a previously employed, intuitive energetic cost of the thermal machine driving suffers from a fundamental flaw, which we resolve with an alternative construction for the cost function. Our DL-quantum control framework can be utilized to solve other quantum dynamics and thermodynamics problems. |
Wednesday, March 16, 2022 8:48AM - 9:24AM |
M09.00005: On Explaining the Surprising Success of Reservoir Computing Forecaster of Chaos? The Universal Machine Learning Dynamical System with Contrasts to VAR and DMD Invited Speaker: Erik Bollt Machine learning has become a widely popular and successful paradigm, including for data-driven science. A major application problem is forecasting complex dynamical systems. Artificial neural networks (ANN) have evolved as a clear leading approach, and recurrent neural networks (RNN) are considered to be especially well suited for. In this setting, the echo state networks (ESN) or reservoir computer (RC) have emerged for simplicity and computational advantages. Instead of a fully trained network, an RC trains only read-out weights. However, why and how an RC works at all, despite randomly selected weights is perhaps a surprise. To this end, we analyzes a simplified RC, where the internal activation function is an identity function. We explicitly connect the RC with linear activation and linear read-out to well developed time-series literature on vector autoregressive averages (VAR) that includes theorems on representability through the WOLD theorem, which already perform reasonably for short term forecasts. In the case of a linear activation and now popular quadratic read-out RC, we explicitly connect to a nonlinear VAR (NVAR), which performs quite well. Further, we associate this paradigm to the now widely popular dynamic mode decomposition (DMD), and thus these three are in a sense different faces of the same concept. We illustrate our observations in terms of popular benchmark examples including Mackey-Glass differential delay equations and the Lorenz63 system. |
Wednesday, March 16, 2022 9:24AM - 9:36AM |
M09.00006: Programming Memories and Computations in Recurrent Neural Networks Without Training Jason Z Kim, Zhixin Lu, Danielle S Bassett Recurrent neural networks (RNNs) perform unique and powerful computations through the internal dynamics of their hidden states. Such dynamics are crucial for cognitive processes that rely on the formation and control of mental representations such as working memory and spatial navigation. While substantial progress has been made in training RNNs, we still lack a fundamental understanding of the native language of recurrent and distributed representations. Here we provide such an understanding and language to the extent of programming the RNN connections to store and modify internal memories without training. Specifically, we use tools from dynamical systems and control to track the dynamical variables of inputs as they propagate through the RNN. We then use the distributed representation of variables in the neurons to program the RNN connection weights to store memories and precise modifications to these memories without actually simulating or training the RNN. Equipped with this language of distributed representation, we answer fundamental questions about the learnability of memories and storage capacity of RNNs as a function of the number of neurons and initial connectivity architecture, thereby enabling the principled design of RNNs for specific applications. |
Wednesday, March 16, 2022 9:36AM - 9:48AM |
M09.00007: Learning the hidden rheology of complex fluids through MF-RhIGNet: Multi Fidelity Rheology-Informed Graph Neural Network Mohammadamin Mahmoudabadbozchelou, Krutarth M Kamani, Simon A Rogers, Safa Jamali Precise and reliable prediction of a structured fluids' response to an applied deformation or stress is of great interest in a variety of industries, particularly in the design of new soft materials and their processes. Nonetheless, that requires solving non-trivial time and rate-dependent constitutive equations that are commonly written in form of coupled differential equations under different flow conditions. In practice, this involves a series of experimental tests to recover model parameters and a subsequent solution of constitutive equations to predict the rheological behavior of a multi-variant thixotropic or viscoelastic material. We present a Multi Fidelity Rheology-Informed Graph Neural Network (MF-RhIGNet) for data-driven constitutive meta-modeling of these complex fluids, by combining observational and inductive biases in the neural network to adhere to constitutive laws of interest. The proposed MF-RhIGNet consists of a low-fidelity part named RhIGNets that is used to learn and recover the hidden rheology of complex constitutive models with multiple coupled ODEs, as well as a high-fidelity part that deals with a limited number of experimental data. MF-RhIGNets are found to be capable of learning and predicting non-trivial behaviors of a complex material using only a handful of data points from a single flow procedure, allowing for accurate modeling with a small number of experiments at unprecedented accuracies. |
Wednesday, March 16, 2022 9:48AM - 10:00AM |
M09.00008: Rheology-informed neural networks for non-local granular flows Milad Saadat, Mohammadamin Mahmoudabadbozchelou, Safa Jamali Constitutive equations describing the rheology of complex fluids commonly construct relationships between the stress tensor at a given location and its dependence on the shear rate at the very same location; however, it is now well understood that in some complex systems, the stress response of a fluid element also depends on the length scales far beyond its immediate neighborhood. For instance, the existence of non-vanishing creeping flows in regions below the yield stress threshold and the dependence of the yield stress on the thickness of the deposited granular matter cannot be accurately described by local rheology. These have resulted in the development of a non-local rheology framework relevant to a wide range of applications with inevitable challenges in its model development and verification. To alleviate these challenges and get the most from relatively scarce experimental data, we developed rheology-informed neural networks (RhiNNs) platforms to describe the non-local rheology of granular flows effectively. By introducing physical intuitions into the existing data-driven approaches usually uninformed of the physical domain, we wish to capture the non-locality of granular flows by solving their constitutive equations, which are demanding to tackle through numerical methods or may even be misleading with locality assumptions or simple Deep Neural Networks (DNNs). Here, in the forward problem, the existing non-local constitutive equations with appropriate boundary and initial conditions are used to solve the stress field. In the inverse problem, though, limited sample data are fed into RhiNN to pinpoint the unknown parameters of underlying assumed constitutive equations. The combination of the forward and inverse problems in RhiNNs may shed light on the rather tricky nature of non-local rheology of granular flows and provide the community with a versatile, easy-to-use alternative to computationally expensive numerical frameworks. |
Wednesday, March 16, 2022 10:00AM - 10:12AM |
M09.00009: Machine Learning for Robot Locomotion in Flowable Materials Daniel Soto, Andras Karsai, Daniel I Goldman, Sehoon Ha, Tingnan Zhang Recent studies of robot movement in flowable granular media (inspired by difficulties faced by extraterrestrial rovers) reveal a coupled locomotor/substrate effect (Shrivastava et al., Sci. Rob. 2020) where the robot spontaneously remodels its environment; this strong coupling occurs in certain limb/wheel movement patterns and results in a localized granular flow allowing the robot to effectively “swim” up highly flowable slopes. However, these gaits were discovered via trial and error by human operators. To accelerate the discovery of effective gaits in flowable frictional media, we use a neural net-based machine learning (ML) scheme to characterize the gait and terrain interactions. We capture the robot kinematics and its surrounding terrain deformation using external depth cameras and train an ML model to describe the coupling of the robot/terrain system. The ML approach for the substrate flow offers an approximate numerical model of the environment that learns from terrain data, circumventing the need for computationally costly continuum models for frictional material. Our scheme may improve robot mobility in situ for real-world environments by offering adaptability to flowable terrain via rapid learning. |
Wednesday, March 16, 2022 10:12AM - 10:24AM |
M09.00010: Predicting a clog: finding signatures of clog formation in hopper flow using machine learning methods Jesse M Hanlan, Sam J Dillavou, Andrea J Liu, Douglas J Durian If a bucket is filled with grains and a hole is cut in the bottom, the grains will flow out of this makeshift hopper. In contrast to a fluid like water, this hopper flow exhibits some unusual properties. With water, the flow rate decreases with the fill height as the pressure falls, but the granular flow rate is constant; that is, until the whole system suddenly arrests due to a clog at the outlet. Previous work by Thomas and Durian (PRL 2015) suggests that this hopper flow is Poissonian, where the system samples microstates until it finds one that can cause a clog. Koivisto and Durian (PRE 2017) then found the microstates being sampled are primarily configuration states, rather than momenta states. So what causes this sudden transition from a flowing state to a clogged one? In order to capture the incredibly large configuration space of grain positions, we constructed an automated, self refilling hopper. We then pair our large data set with machine learning techniques in order to explore general signatures of clog formation within granular flows. |
Wednesday, March 16, 2022 10:24AM - 10:36AM |
M09.00011: Using analogical reasoning to build transferable models Cody L Petrie, Christian N Anderson, Casie Maekawa, Travis Maekawa, Mark K Transtrum Humans use analogical reasoning to connect understanding of one system to another. Can machines use similar abstractions to transfer their learning from training data to other regimes? The Manifold Boundary Approximation Method constructs simple, reduced models of target phenomena in a data-driven way. We consider the set of all such reduced models and use the topological relationships among them to reason about model selection for new, unobserved phenomena. Given minimal models for several target behaviors, we introduce the supremum principle as a criterion for selecting a new, transferable model. The supremum principle shares connections with the theory of analogical reasoning in cognitive psychology. Having unified the relevant mechanisms, the supremal model, i.e., the least upper bound, is the simplest model that reduces to each of the target behaviors. Describing multiple behavioral regimes, the supremal model provides a controller to move between various states of interest, e.g., sick and healthy cells in systems biology. Additionally, the supremal model transfers to domains outside of the training data, allowing it to describe new, emergent behaviors. We present a general algorithm for constructing a supremal model and demonstrate with examples from various disciplines. |
Wednesday, March 16, 2022 10:36AM - 10:48AM |
M09.00012: Evidence for Griffiths Phase Criticality in Residual Neural Networks Logan G Wright, Maxwell Anderson, Peter L McMahon Research on synthetic and biological neural networks shows that they operate robustly near phase transitions. Griffiths phases, stretched configuration regions with critical behavior that exist for heterogeneously structured networks, are a proposed explanation for how this occurs. Meanwhile, by adding identity "skip" connections to feedforward neural networks, researchers in deep learning have developed Residual Neural Networks (ResNet) that can be reliably trained to unprecedented depths, a property that in conventional networks only occurs precisely at criticality. Here we show that the Griffiths phase concept is indeed related to these behaviors in ResNets when configured with sufficient normalization/weight variance. Here, by measuring output scaling and examining the structure of random networks, we show that ResNets display the same topological signatures and extended region of relaxed scaling observed in Griffith phase criticality, while conventional feedforward networks do not. These results shed light on why ResNets operate so robustly, the role of normalization layers now common in deep learning architectures, and suggests how future models could be better understood (including more recent ResNet-based models) or designed. |
Wednesday, March 16, 2022 10:48AM - 11:00AM |
M09.00013: Capturing Strain Induced Orthotropy Through a Novel Free Energy Density Definition Alex G Arzoumanidis The work is a specific implementation of Schapery’s Thermodynamics based approach to viscoelasticity and mechanics. The change in free energy density from mechanical deformation is presented as a function of logarithmic principal strains. Principal strain calculation provides 3 of the 9 mathematical relationships needed to capture strain induced orthotropy. The proposed strain energy density is then made up of 6 separate functions, each defining an independent sub-state in terms of a single strain. Three sub-state functions are dependent on each of the principal strains. These axial contributions reduce to the dilatational contribution to 3D stress for isotropic materials. Three distortional sub-state functions are each defined in terms of the stretch ratios on each principal plane. The derivative of the proposed free energy density function cleanly separates distortion from axial (dilatational) stress in the large strain stress-strain response. Based in thermodynamics, the approach provides a mathematical framework for scaling MD simulations up to the continuum level. |
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