arXiv subjects

Petros Koumoutsakos

Publications and source records attributed to Petros Koumoutsakos.

At least 55 records · Page 3Linked to original sources

arXiv2023

Interpretable reduced-order modeling with time-scale separation

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction crucial. We propose such a data-driven scheme that automates the identification of the time-scales involved and can produce stable predictions forward in time as well as under different initial conditions not included in the training data. To this end, we combine a non-linear autoencoder architecture with a time-continuous model for the latent dynamics in the complex space. It readily allows for the inclusion of sparse and irregularly sampled training data. The learned, latent dynamics are interpretable and reveal the different temporal scales involved. We show that this data-driven scheme can automatically learn the independent processes that decompose a system of linear ODEs along the eigenvectors of the system's matrix. Apart from this, we demonstrate the applicability of the proposed framework in a hidden Markov Model and the (discretized) Kuramoto-Shivashinsky (KS) equation. Additionally, we propose a probabilistic version, which captures predictive uncertainties and further improves upon the results of the deterministic framework.

stat.ML↗

arXiv2023

Learning from Predictions: Fusing Training and Autoregressive Inference for Long-Term Spatiotemporal Forecasts

Recurrent Neural Networks (RNNs) have become an integral part of modeling and forecasting frameworks in areas like natural language processing and high-dimensional dynamical systems such as turbulent fluid flows. To improve the accuracy of predictions, RNNs are trained using the Backpropagation Through Time (BPTT) method to minimize prediction loss. During testing, RNNs are often used in autoregressive scenarios where the output of the network is fed back into the input. However, this can lead to the exposure bias effect, as the network was trained to receive ground-truth data instead of its own predictions. This mismatch between training and testing is compounded when the state distributions are different, and the train and test losses are measured. To address this, previous studies have proposed solutions for language processing networks with probabilistic predictions. Building on these advances, we propose the Scheduled Autoregressive BPTT (BPTT-SA) algorithm for predicting complex systems. Our results show that BPTT-SA effectively reduces iterative error propagation in Convolutional RNNs and Convolutional Autoencoder RNNs, and demonstrate its capabilities in long-term prediction of high-dimensional fluid flows.

cs.LG↗

arXiv2022

Remember and Forget Experience Replay for Multi-Agent Reinforcement Learning

We present the extension of the Remember and Forget for Experience Replay (ReF-ER) algorithm to Multi-Agent Reinforcement Learning (MARL). ReF-ER was shown to outperform state of the art algorithms for continuous control in problems ranging from the OpenAI Gym to complex fluid flows. In MARL, the dependencies between the agents are included in the state-value estimator and the environment dynamics are modeled via the importance weights used by ReF-ER. In collaborative environments, we find the best performance when the value is estimated using individual rewards and we ignore the effects of other actions on the transition map. We benchmark the performance of ReF-ER MARL on the Stanford Intelligent Systems Laboratory (SISL) environments. We find that employing a single feed-forward neural network for the policy and the value function in ReF-ER MARL, outperforms state of the art algorithms that rely on complex neural network architectures.

cs.LG↗

arXiv2022

CubismAMR -- A C++ library for Distributed Block-Structured Adaptive Mesh Refinement

We present CubismAMR, a C++ library for distributed simulations with block-structured grids and Adaptive Mesh Refinement. A numerical method to solve the incompressible Navier-Stokes equations is proposed, that comes with a novel approach of solving the pressure Poisson equation on an adaptively refined grid. Validation and verification results for the method are presented, for the flow past an impulsively started cylinder.

physics.flu-dyn↗

arXiv2022

Optimizing a DIscrete Loss (ODIL) to solve forward and inverse problems for partial differential equations using machine learning tools

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals that are solved using gradient descent and Newton's methods. We demonstrate the value of this approach on equations that may have missing parameters or where no sufficient data is available to form a well-posed initial-value problem. The framework is presented for mesh based discretizations of PDEs and inherits their accuracy, convergence, and conservation properties. It preserves the sparsity of the solutions and is readily applicable to inverse and ill-posed problems. It is applied to PDE-constrained optimization, optical flow, system identification, and data assimilation using gradient descent algorithms including those often deployed in machine learning. We compare ODIL with related approach that represents the solution with neural networks. We compare the two methodologies and demonstrate advantages of ODIL that include significantly higher convergence rates and several orders of magnitude lower computational cost. We evaluate the method on various linear and nonlinear partial differential equations including the Navier-Stokes equations for flow reconstruction problems.

math.NA↗

arXiv2022

Scientific multi-agent reinforcement learning for wall-models of turbulent flows

The predictive capabilities of turbulent flow simulations, critical for aerodynamic design and weather prediction, hinge on the choice of turbulence models. The abundance of data from experiments and simulations and the advent of machine learning have provided a boost to turbulence modeling efforts. However, simulations of turbulent flows remain hindered by the inability of heuristics and supervised learning to model the near-wall dynamics. We address this challenge by introducing scientific multi-agent reinforcement learning (SciMARL) for the discovery of wall models for large-eddy simulations (LES). In SciMARL, discretization points act also as cooperating agents that learn to supply the LES closure model. The agents self-learn using limited data and generalize to extreme Reynolds numbers and previously unseen geometries. The present simulations reduce by several orders of magnitude the computational cost over fully-resolved simulations while reproducing key flow quantities. We believe that SciMARL creates unprecedented capabilities for the simulation of turbulent flows.

physics.flu-dyn↗

arXiv2022

Independent Control and Path Planning of Microswimmers with a Uniform Magnetic Field

Artificial bacteria flagella (ABFs) are magnetic helical micro-swimmers that can be remotely controlled via a uniform, rotating magnetic field. Previous studies have used the heterogeneous response of microswimmers to external magnetic fields for achieving independent control. Here we introduce analytical and reinforcement learning control strategies for path planning to a target by multiple swimmers using a uniform magnetic field. The comparison of the two algorithms shows the superiority of reinforcement learning in achieving minimal travel time to a target. The results demonstrate, for the first time, the effective independent navigation of realistic micro-swimmers with a uniform magnetic field in a viscous flow field.

physics.flu-dyn↗

arXiv2021

Multiscale Simulations of Complex Systems by Learning their Effective Dynamics

Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively parallel simulations predict the system dynamics by resolving all spatiotemporal scales, often at a cost that prevents experimentation while their findings may not allow for generalisation. On the other hand reduced order models are fast but limited by the frequently adopted linearization of the system dynamics and/or the utilization of heuristic closures. Here we present a novel systematic framework that bridges large scale simulations and reduced order models to Learn the Effective Dynamics (LED) of diverse complex systems. The framework forms algorithmic alloys between non-linear machine learning algorithms and the Equation-Free approach for modeling complex systems. LED deploys autoencoders to formulate a mapping between fine and coarse-grained representations and evolves the latent space dynamics using recurrent neural networks. The algorithm is validated on benchmark problems and we find that it outperforms state of the art reduced order models in terms of predictability and large scale simulations in terms of cost. LED is applicable to systems ranging from chemistry to fluid mechanics and reduces the computational effort by up to two orders of magnitude while maintaining the prediction accuracy of the full system dynamics. We argue that LED provides a novel potent modality for the accurate prediction of complex systems.

physics.comp-ph↗

arXiv2021

Learning swimming escape patterns for larval fish under energy constraints

Swimming organisms can escape their predators by creating and harnessing unsteady flow fields through their body motions. Stochastic optimization and flow simulations have identified escape patterns that are consistent with those observed in natural larval swimmers. However, these patterns have been limited by the specification of a particular cost function and depend on a prescribed functional form of the body motion. Here, we deploy reinforcement learning to discover swimmer escape patterns for larval fish under energy constraints. The identified patterns include the C-start mechanism, in addition to more energetically efficient escapes. We find that maximizing distance with limited energy requires swimming via short bursts of accelerating motion interlinked with phases of gliding. The present, data efficient, reinforcement learning algorithm results in an array of patterns that reveal practical flow optimization principles for efficient swimming and the methodology can be transferred to the control of aquatic robotic devices operating under energy constraints.

physics.flu-dyn↗

arXiv2021

A computational study of expiratory particle transport and vortex dynamics during breathing with and without face masks

We present high-fidelity numerical simulations of expiratory biosol transport during normal breathing under indoor, stagnant air conditions with and without a facial mask. We investigate mask efficacy to suppress the spread of saliva particles that is underpinnings existing social distancing recommendations. The present simulations incorporate the effect of human anatomy and consider a spectrum of saliva particulate sizes that ranges from 0.1 micrometers to 10 micrometers while accounting also for their evaporation. The simulations elucidate the vorticity dynamics of human breathing and show that without a facial mask, saliva particulates could travel over 2.2 m away from the person. However, a non-medical grade face mask can drastically reduce saliva particulate propagation to 0.72 m away from the person. This study provides new quantitative evidence that facial masks can successfully suppress the spreading of saliva particulates due to normal breathing in indoor environments.

physics.flu-dyn↗

arXiv2021

Korali: Efficient and Scalable Software Framework for Bayesian Uncertainty Quantification and Stochastic Optimization

We present Korali, an open-source framework for large-scale Bayesian uncertainty quantification and stochastic optimization. The framework relies on non-intrusive sampling of complex multiphysics models and enables their exploitation for optimization and decision-making. In addition, its distributed sampling engine makes efficient use of massively-parallel architectures while introducing novel fault tolerance and load balancing mechanisms. We demonstrate these features by interfacing Korali with existing high-performance software such as Aphros, Lammps (CPU-based), and Mirheo (GPU-based) and show efficient scaling for up to 512 nodes of the CSCS Piz Daint supercomputer. Finally, we present benchmarks demonstrating that Korali outperforms related state-of-the-art software frameworks.

cs.DC↗

arXiv2021

Computing foaming flows across scales: from breaking waves to microfluidics

Crashing ocean waves, cappuccino froths and microfluidic bubble crystals are examples of foamy flows. Foamy flows are critical in numerous natural and industrial processes and remain notoriously difficult to compute as they involve coupled, multiscale physical processes. Computations need to resolve the interactions of the bubbles with the fluid and complex boundaries, while capturing the drainage and rupture of the microscopic liquid films at their interface. We present a novel multilayer simulation framework (Multi-VOF) that advances the state of the art in simulation capabilities of foamy flows. The framework introduces a novel scheme for the distinct handling of multiple neighboring bubbles and a new regularization method that produces sharp interfaces and removes spurious fragments. Multi-VOF is verified and validated with experimental results and complemented with open source, efficient scalable software. We demonstrate capturing of bubble crystalline structures in realistic microfluidics devices and foamy flows involving tens of thousands of bubbles in a waterfall. The present multilayer framework extends the classical volume-of-fluid methodology and allows for unprecedented large scale, predictive simulations of flows with multiple interfaces.

physics.comp-ph↗

arXiv2021

Learning Efficient Navigation in Vortical Flow Fields

Efficient point-to-point navigation in the presence of a background flow field is important for robotic applications such as ocean surveying. In such applications, robots may only have knowledge of their immediate surroundings or be faced with time-varying currents, which limits the use of optimal control techniques for planning trajectories. Here, we apply a novel Reinforcement Learning algorithm to discover time-efficient navigation policies to steer a fixed-speed swimmer through an unsteady two-dimensional flow field. The algorithm entails inputting environmental cues into a deep neural network that determines the swimmer's actions, and deploying Remember and Forget Experience replay. We find that the resulting swimmers successfully exploit the background flow to reach the target, but that this success depends on the type of sensed environmental cue. Surprisingly, a velocity sensing approach outperformed a bio-mimetic vorticity sensing approach by nearly two-fold in success rate. Equipped with local velocity measurements, the reinforcement learning algorithm achieved near 100% success in reaching the target locations while approaching the time-efficiency of paths found by a global optimal control planner.

physics.flu-dyn↗

arXiv2021

Accelerated Simulations of Molecular Systems through Learning of their Effective Dynamics

Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the timescales necessary to capture the structural evolution of bio-molecules remains a daunting task. In this work we present a novel framework to advance simulation timescales by up to three orders of magnitude, by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the Müeller-Brown potential, the Trp Cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations and can generate, at any instant, the respective all-atom molecular trajectories. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.

physics.comp-ph↗

arXiv2020

Automating Turbulence Modeling by Multi-Agent Reinforcement Learning

The modeling of turbulent flows is critical to scientific and engineering problems ranging from aircraft design to weather forecasting and climate prediction. Over the last sixty years numerous turbulence models have been proposed, largely based on physical insight and engineering intuition. Recent advances in machine learning and data science have incited new efforts to complement these approaches. To date, all such efforts have focused on supervised learning which, despite demonstrated promise, encounters difficulties in generalizing beyond the distributions of the training data. In this work we introduce multi-agent reinforcement learning (MARL) as an automated discovery tool of turbulence models. We demonstrate the potential of this approach on Large Eddy Simulations of homogeneous and isotropic turbulence using as reward the recovery of the statistical properties of Direct Numerical Simulations. Here, the closure model is formulated as a control policy enacted by cooperating agents, which detect critical spatio-temporal patterns in the flow field to estimate the unresolved sub-grid scale (SGS) physics. The present results are obtained with state-of-the-art algorithms based on experience replay and compare favorably with established dynamic SGS modeling approaches. Moreover, we show that the present turbulence models generalize across grid sizes and flow conditions as expressed by the Reynolds numbers.

physics.comp-ph↗

arXiv2020

Improved Memories Learning

We propose Improved Memories Learning (IMeL), a novel algorithm that turns reinforcement learning (RL) into a supervised learning (SL) problem and delimits the role of neural networks (NN) to interpolation. IMeL consists of two components. The first is a reservoir of experiences. Each experience is updated based on a non-parametric procedural improvement of the policy, computed as a bounded one-sample Monte Carlo estimate. The second is a NN regressor, which receives as input improved experiences from the reservoir (context points) and computes the policy by interpolation. The NN learns to measure the similarity between states in order to compute long-term forecasts by averaging experiences, rather than by encoding the problem structure in the NN parameters. We present preliminary results and propose IMeL as a baseline method for assessing the merits of more complex models and inductive biases.

cs.LG↗

arXiv2020

Data-driven prediction and origin identification of epidemics in population networks

Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework to infer model parameters for a disease spreading on a network of communities from limited, noisy observations; the state-of-the-art computational framework compensates for the model complexity by exploiting massively parallel computing architectures. Using noisy, synthetic data, we show the potential of the approach to perform robust model fitting and additionally demonstrate that we can effectively identify the disease origin via Bayesian model selection. As disease-related data are increasingly available, the proposed framework has broad practical relevance for the prediction and management of epidemics.

q-bio.PE↗

arXiv2020

Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics

We examine the efficiency of Recurrent Neural Networks in forecasting the spatiotemporal dynamics of high dimensional and reduced order complex systems using Reservoir Computing (RC) and Backpropagation through time (BPTT) for gated network architectures. We highlight advantages and limitations of each method and discuss their implementation for parallel computing architectures. We quantify the relative prediction accuracy of these algorithms for the longterm forecasting of chaotic systems using as benchmarks the Lorenz-96 and the Kuramoto-Sivashinsky (KS) equations. We find that, when the full state dynamics are available for training, RC outperforms BPTT approaches in terms of predictive performance and in capturing of the long-term statistics, while at the same time requiring much less training time. However, in the case of reduced order data, large scale RC models can be unstable and more likely than the BPTT algorithms to diverge. In contrast, RNNs trained via BPTT show superior forecasting abilities and capture well the dynamics of reduced order systems. Furthermore, the present study quantifies for the first time the Lyapunov Spectrum of the KS equation with BPTT, achieving similar accuracy as RC. This study establishes that RNNs are a potent computational framework for the learning and forecasting of complex spatiotemporal systems.

eess.SP↗