Distributed Gradient Descent with Many Local Steps in Overparameterized Models

In distributed training of machine learning models, gradient descent with local iterative steps is a very popular method, variants of which are commonly known as Local-SGD or the Federated Averaging (FedAvg). In this method, gradient steps based on local datasets are taken independently in distributed compute nodes to update the local models, which are then aggregated intermittently. Although the existing convergence analysis suggests that with heterogeneous data, FedAvg encounters quick performance degradation as the number of local steps increases, it is shown to work quite well in practice, especially in the distributed training of large language models. In this work we try to explain this good performance from a viewpoint of implicit bias in Local Gradient Descent (Local-GD) with a large number of local steps. In overparameterized regime, the gradient descent at each compute node would lead the model to a specific direction locally. We characterize the dynamics of the aggregated global model and compare it to the centralized model trained with all of the data in one place. In particular, we analyze the implicit bias of gradient descent on linear models, for both regression and classification tasks. Our analysis shows that the aggregated global model converges exactly to the centralized model for regression tasks, and converges (in direction) to the same feasible set as centralized model for classification tasks. We further propose a Modified Local-GD with a refined aggregation and theoretically show it converges to the centralized model in direction for linear classification. We empirically verified our theoretical findings in linear models and also conducted experiments on distributed fine-tuning of pretrained neural networks to further apply our theory.

Anvil: An integration of artificial intelligence, sampling techniques, and a combined CAD-CFD tool

In this work, we introduce an open-source integrated CAD-CFD tool, Anvil, which combines FreeCAD for CAD modeling and OpenFOAM for CFD analysis, along with an AI-based optimization method (Bayesian optimization) and other sampling algorithms. Anvil serves as a scientific machine learning tool for shape optimization in three modes: data generation, CFD evaluation, and shape optimization. In data generation mode, it automatically runs CFD evaluations and generates data for training a surrogate model. In optimization mode, it searches for the optimal design under given requirements and optimization metrics. In CFD mode, a single CAD file can be evaluated with a single OpenFOAM run. To use Anvil, experimenters provide a JSON configuration file and a parametric CAD seed design. Anvil can be used to study solid-fluid dynamics for any subsonic flow conditions and has been demonstrated in various simulation and optimization use cases. The open-source code for the tool, installation process, artifacts (such as CAD seed designs and example STL models), experimentation results, and detailed documentation can be found at \url{https://github.com/symbench/Anvil}.

Sample-Efficient and Surrogate-Based Design Optimization of Underwater Vehicle Hulls

Physics simulations are a computational bottleneck in computer-aided design (CAD) optimization processes. Hence, in order to make accurate (computationally expensive) simulations feasible for use in design optimization, one requires either an optimization framework that is highly sample-efficient or fast data-driven proxies (surrogate models) for long running simulations. In this work, we leverage recent advances in optimization and artificial intelligence (AI) to address both of these potential solutions, in the context of designing an optimal unmanned underwater vehicle (UUV). We first investigate and compare the sample efficiency and convergence behavior of different optimization techniques with a standard computational fluid dynamics (CFD) solver in the optimization loop. We then develop a deep neural network (DNN) based surrogate model to approximate drag forces that would otherwise be computed via direct numerical simulation with the CFD solver. The surrogate model is in turn used in the optimization loop of the hull design. Our study finds that the Bayesian Optimization Lower Condition Bound (BO LCB) algorithm is the most sample-efficient optimization framework and has the best convergence behavior of those considered. Subsequently, we show that our DNN-based surrogate model predicts drag force on test data in tight agreement with CFD simulations, with a mean absolute percentage error (MAPE) of 1.85%. Combining these results, we demonstrate a two-orders-of-magnitude speedup (with comparable accuracy) for the design optimization process when the surrogate model is used. To our knowledge, this is the first study applying Bayesian optimization and DNN-based surrogate modeling to the problem of UUV design optimization, and we share our developments as open-source software.

Constrained Bayesian Optimization for Automatic Underwater Vehicle Hull Design

Automatic underwater vehicle hull Design optimization is a complex engineering process for generating a UUV hull with optimized properties on a given requirement. First, it involves the integration of involved computationally complex engineering simulation tools. Second, it needs integration of a sample efficient optimization framework with the integrated toolchain. To this end, we integrated the CAD tool called FreeCAD with CFD tool openFoam for automatic design evaluation. For optimization, we chose Bayesian optimization (BO), which is a well-known technique developed for optimizing time-consuming expensive engineering simulations and has proven to be very sample efficient in a variety of problems, including hyper-parameter tuning and experimental design. During the optimization process, we can handle infeasible design as constraints integrated into the optimization process. By integrating domain-specific toolchain with AI-based optimization, we executed the automatic design optimization of underwater vehicle hull design. For empirical evaluation, we took two different use cases of real-world underwater vehicle design to validate the execution of our tool.

Fusion of ML with numerical simulation for optimized propeller design

In computer-aided engineering design, the goal of a designer is to find an optimal design on a given requirement using the numerical simulator in loop with an optimization method. In this design optimization process, a good design optimization process is one that can reduce the time from inception to design. In this work, we take a class of design problem, that is computationally cheap to evaluate but has high dimensional design space. In such cases, traditional surrogate-based optimization does not offer any benefits. In this work, we propose an alternative way to use ML model to surrogate the design process that formulates the search problem as an inverse problem and can save time by finding the optimal design or at least a good initial seed design for optimization. By using this trained surrogate model with the traditional optimization method, we can get the best of both worlds. We call this as Surrogate Assisted Optimization (SAO)- a hybrid approach by mixing ML surrogate with the traditional optimization method. Empirical evaluations of propeller design problems show that a better efficient design can be found in fewer evaluations using SAO.

Search for universal minimum drag resistance underwater vehicle hull using CFD

In Autonomous Underwater Vehicles (AUVs) design, hull resistance is an important factor in determining the power requirements and range of vehicle and consequently affect battery size, weight, and volume requirement of the design. In this paper, we leverage on AI-based optimization algorithm along with Computational Fluid Dynamics (CFD) simulation to study the optimal hull design that minimizing the resistance. By running the CFD-based optimization at different operating velocities and turbulence intensity, we want to study/search the possibility of a universal design that will provide least resistance/near-optimal design across all operating conditions (operating velocity) and environmental conditions (turbulence intensity). Early result demonstrated that the optimal design found at low velocity and low turbulence condition performs very poor at high velocity and high turbulence conditions. However, a design that is optimal at high velocity and high turbulence conditions performs near-optimal across many considered velocity and turbulence conditions.

Async-HFL: Efficient and Robust Asynchronous Federated Learning in Hierarchical IoT Networks

Federated Learning (FL) has gained increasing interest in recent years as a distributed on-device learning paradigm. However, multiple challenges remain to be addressed for deploying FL in real-world Internet-of-Things (IoT) networks with hierarchies. Although existing works have proposed various approaches to account data heterogeneity, system heterogeneity, unexpected stragglers and scalibility, none of them provides a systematic solution to address all of the challenges in a hierarchical and unreliable IoT network. In this paper, we propose an asynchronous and hierarchical framework (Async-HFL) for performing FL in a common three-tier IoT network architecture. In response to the largely varied delays, Async-HFL employs asynchronous aggregations at both the gateway and the cloud levels thus avoids long waiting time. To fully unleash the potential of Async-HFL in converging speed under system heterogeneities and stragglers, we design device selection at the gateway level and device-gateway association at the cloud level. Device selection chooses edge devices to trigger local training in real-time while device-gateway association determines the network topology periodically after several cloud epochs, both satisfying bandwidth limitation. We evaluate Async-HFL's convergence speedup using large-scale simulations based on ns-3 and a network topology from NYCMesh. Our results show that Async-HFL converges 1.08-1.31x faster in wall-clock time and saves up to 21.6% total communication cost compared to state-of-the-art asynchronous FL algorithms (with client selection). We further validate Async-HFL on a physical deployment and observe robust convergence under unexpected stragglers.

Data efficient surrogate modeling for engineering design: Ensemble-free batch mode deep active learning for regression

In a computer-aided engineering design optimization problem that involves notoriously complex and time-consuming simulator, the prevalent approach is to replace these simulations with a data-driven surrogate that approximates the simulator's behavior at a much cheaper cost. The main challenge in creating an inexpensive data-driven surrogate is the generation of a sheer number of data using these computationally expensive numerical simulations. In such cases, Active Learning (AL) methods have been used that attempt to learn an input--output behavior while labeling the fewest samples possible. The current trend in AL for a regression problem is dominated by the Bayesian framework that needs training an ensemble of learning models that makes surrogate training computationally tedious if the underlying learning model is Deep Neural Networks (DNNs). However, DNNs have an excellent capability to learn highly nonlinear and complex relationships even for a very high dimensional problem. To leverage the excellent learning capability of deep networks along with avoiding the computational complexity of the Bayesian paradigm, in this work we propose a simple and scalable approach for active learning that works in a student-teacher manner to train a surrogate model. By using this proposed approach, we are able to achieve the same level of surrogate accuracy as the other baselines like DBAL and Monte Carlo sampling with up to 40 % fewer samples. We empirically evaluated this method on multiple use cases including three different engineering design domains:finite element analysis, computational fluid dynamics, and propeller design.

DeepAL for Regression Using $ε$-weighted Hybrid Query Strategy

Designing an inexpensive approximate surrogate model that captures the salient features of an expensive high-fidelity behavior is a prevalent approach in design optimization. In recent times, Deep Learning (DL) models are being used as a promising surrogate computational model for engineering problems. However, the main challenge in creating a DL-based surrogate is to simulate/label a large number of design points, which is time-consuming for computationally costly and/or high-dimensional engineering problems. In the present work, we propose a novel sampling technique by combining the active learning (AL) method with DL. We call this method $\epsilon$-weighted hybrid query strategy ($\epsilon$-HQS) , which focuses on the evaluation of the surrogate at each learning iteration and provides an estimate of the failure probability of the surrogate in the Design Space. By reusing already collected training and test data, the learned failure probability guides the next iteration's sampling process to the region of the high probability of failure. During the empirical evaluation, better accuracy of the surrogate was observed in comparison to other methods of sample selection. We empirically evaluated this method in two different engineering design domains, finite element based static stress analysis of submarine pressure vessel(computationally costly process) and second submarine propeller design( high dimensional problem). https://github.com/vardhah/epsilon_weighted_Hybrid_Query_Strategy

Reduced Robust Random Cut Forest for Out-Of-Distribution detection in machine learning models

Most machine learning-based regressors extract information from data collected via past observations of limited length to make predictions in the future. Consequently, when input to these trained models is data with significantly different statistical properties from data used for training, there is no guarantee of accurate prediction. Consequently, using these models on out-of-distribution input data may result in a completely different predicted outcome from the desired one, which is not only erroneous but can also be hazardous in some cases. Successful deployment of these machine learning models in any system requires a detection system, which should be able to distinguish between out-of-distribution and in-distribution data (i.e. similar to training data). In this paper, we introduce a novel approach for this detection process using a Reduced Robust Random Cut Forest (RRRCF) data structure, which can be used on both small and large data sets. Similar to the Robust Random Cut Forest (RRCF), RRRCF is a structured, but a reduced representation of the training data sub-space in form of cut trees. Empirical results of this method on both low and high-dimensional data showed that inference about data being in/out of training distribution can be made efficiently and the model is easy to train with no difficult hyper-parameter tuning. The paper discusses two different use-cases for testing and validating results.