We harness the physics-informed neural network (PINN) approach to extend the utility of phenomenological models for particle migration in shear flow. Specifically, we propose to constrain the neural network training via a model for the physics of shear-induced particle migration in suspensions. Then, we train the PINN against experimental data from the literature, showing that this approach provides both better fidelity to the experiments, and a novel understanding of the relative roles of the hypothesized migration fluxes. We first verify the PINN approach for solving the inverse problem of radial particle migration in a non-Brownian suspension in an annular Couette flow. In this classical case, the PINN yields the same value (as reported in the literature) for the ratio of the two parameters of the empirical model. Next, we apply the PINN approach to analyze experiments on particle migration in both non-Brownian and Brownian suspensions in Poiseuille slot flow, for which a definitive calibration of the phenomenological migration model has been lacking. Using the PINN approach, we identify the unknown/empirical parameters in the physical model through the inverse solver capability of PINNs. Specifically, the values are significantly different from those for the Couette cell, highlighting an inconsistency in the literature that uses the latter value for Poiseuille flow. Importantly, the PINN results also show that the inferred values of the empirical model's parameters vary with the shear P\'eclet number and the particle bulk volume fraction of the suspension, instead of being constant as assumed in some previous literature.
相關內容
Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會議。
Publisher：IFIP。
SIT：
Nonhomogeneous partial differential equations (PDEs) are an applicable model in soft sensor modeling for describing spatiotemporal industrial systems with unmeasurable source terms, which cannot be well solved by existing physics-informed neural networks (PINNs). To this end, a coupled PINN (CPINN) with a recurrent prediction (RP) learning strategy (CPINN-RP) is proposed for soft sensor modeling in spatiotemporal industrial processes, such as vibration displacement. First, CPINN containing NetU and NetG is proposed. NetU is used to approximate the solutions to PDEs under study and NetG is used to regularize the training of NetU. The two networks are integrated into a data-physics-hybrid loss function. Then, we theoretically prove that the proposed CPINN has a satisfying approximation capacity to the PDEs solutions. Besides the theoretical aspects, we propose a hierarchical training strategy to optimize and couple the two networks to achieve the parameters of CPINN. Secondly, NetU-RP is achieved by NetU compensated by RP, the recurrently delayed output of CPINN, to further improve the soft sensor performance. Finally, simulations and experiment verify the effectiveness and practical applications of CPINN-RP.
The proliferation of automated data collection schemes and the advances in sensorics are increasing the amount of data we are able to monitor in real-time. However, given the high annotation costs and the time required by quality inspections, data is often available in an unlabeled form. This is fostering the use of active learning for the development of soft sensors and predictive models. In production, instead of performing random inspections to obtain product information, labels are collected by evaluating the information content of the unlabeled data. Several query strategy frameworks for regression have been proposed in the literature but most of the focus has been dedicated to the static pool-based scenario. In this work, we propose a new strategy for the stream-based scenario, where instances are sequentially offered to the learner, which must instantaneously decide whether to perform the quality check to obtain the label or discard the instance. The approach is inspired by the optimal experimental design theory and the iterative aspect of the decision-making process is tackled by setting a threshold on the informativeness of the unlabeled data points. The proposed approach is evaluated using numerical simulations and the Tennessee Eastman Process simulator. The results confirm that selecting the examples suggested by the proposed algorithm allows for a faster reduction in the prediction error.
An important aspect of developing reliable deep learning systems is devising strategies that make these systems robust to adversarial attacks. There is a long line of work that focuses on developing defenses against these attacks, but recently, researchers have began to study ways to reverse engineer the attack process. This allows us to not only defend against several attack models, but also classify the threat model. However, there is still a lack of theoretical guarantees for the reverse engineering process. Current approaches that give any guarantees are based on the assumption that the data lies in a union of linear subspaces, which is not a valid assumption for more complex datasets. In this paper, we build on prior work and propose a novel framework for reverse engineering of deceptions which supposes that the clean data lies in the range of a GAN. To classify the signal and attack, we jointly solve a GAN inversion problem and a block-sparse recovery problem. For the first time in the literature, we provide deterministic linear convergence guarantees for this problem. We also empirically demonstrate the merits of the proposed approach on several nonlinear datasets as compared to state-of-the-art methods.
In this paper, we examine the problem of partial inference in the context of structured prediction. Using a generative model approach, we consider the task of maximizing a score function with unary and pairwise potentials in the space of labels on graphs. Employing a two-stage convex optimization algorithm for label recovery, we analyze the conditions under which a majority of the labels can be recovered. We introduce a novel perspective on the Karush-Kuhn-Tucker (KKT) conditions and primal and dual construction, and provide statistical and topological requirements for partial recovery with provable guarantees.
Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this work, we contribute an analysis of the loss landscape for GP models using methods from physics. We demonstrate $\nu$-continuity for Matern kernels and outline aspects of catastrophe theory at critical points in the loss landscape. By directly including $\nu$ in the hyperparameter optimisation for Matern kernels, we find that typical values of $\nu$ are far from optimal in terms of performance, yet prevail in the literature due to the increased computational speed. We also provide an a priori method for evaluating the effect of GP ensembles and discuss various voting approaches based on physical properties of the loss landscape. The utility of these approaches is demonstrated for various synthetic and real datasets. Our findings provide an enhanced understanding of the decision-making process behind GPs and offer practical guidance for improving their performance and interpretability in a range of applications.
Neural networks are universal approximators and are studied for their use in solving differential equations. However, a major criticism is the lack of error bounds for obtained solutions. This paper proposes a technique to rigorously evaluate the error bound of Physics-Informed Neural Networks (PINNs) on most linear ordinary differential equations (ODEs), certain nonlinear ODEs, and first-order linear partial differential equations (PDEs). The error bound is based purely on equation structure and residual information and does not depend on assumptions of how well the networks are trained. We propose algorithms that bound the error efficiently. Some proposed algorithms provide tighter bounds than others at the cost of longer run time.
The ongoing deep learning revolution has allowed computers to outclass humans in various games and perceive features imperceptible to humans during classification tasks. Current machine learning techniques have clearly distinguished themselves in specialized tasks. However, we have yet to see robots capable of performing multiple tasks at an expert level. Most work in this field is focused on the development of more sophisticated learning algorithms for a robot's controller given a largely static and presupposed robotic design. By focusing on the development of robotic bodies, rather than neural controllers, I have discovered that robots can be designed such that they overcome many of the current pitfalls encountered by neural controllers in multitask settings. Through this discovery, I also present novel metrics to explicitly measure the learning ability of a robotic design and its resistance to common problems such as catastrophic interference. Traditionally, the physical robot design requires human engineers to plan every aspect of the system, which is expensive and often relies on human intuition. In contrast, within the field of evolutionary robotics, evolutionary algorithms are used to automatically create optimized designs, however, such designs are often still limited in their ability to perform in a multitask setting. The metrics created and presented here give a novel path to automated design that allow evolved robots to synergize with their controller to improve the computational efficiency of their learning while overcoming catastrophic interference. Overall, this dissertation intimates the ability to automatically design robots that are more general purpose than current robots and that can perform various tasks while requiring less computation.
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.
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