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Add to EdgeMiguel A. Bessa
Engineering software 2.0 by interpolating neural networks: unifying training, solving, and calibration
Apr 16, 2024
The evolution of artificial intelligence (AI) and neural network theories has revolutionized the way software is programmed, shifting from a hard-coded series of codes to a vast neural network. However, this transition in engineering software has faced challenges such as data scarcity, multi-modality of data, low model accuracy, and slow inference. Here, we propose a new network based on interpolation theories and tensor decomposition, the interpolating neural network (INN). Instead of interpolating training data, a common notion in computer science, INN interpolates interpolation points in the physical space whose coordinates and values are trainable. It can also extrapolate if the interpolation points reside outside of the range of training data and the interpolation functions have a larger support domain. INN features orders of magnitude fewer trainable parameters, faster training, a smaller memory footprint, and higher model accuracy compared to feed-forward neural networks (FFNN) or physics-informed neural networks (PINN). INN is poised to usher in Engineering Software 2.0, a unified neural network that spans various domains of space, time, parameters, and initial/boundary conditions. This has previously been computationally prohibitive due to the exponentially growing number of trainable parameters, easily exceeding the parameter size of ChatGPT, which is over 1 trillion. INN addresses this challenge by leveraging tensor decomposition and tensor product, with adaptable network architecture.
Gradient-free neural topology optimization
Mar 07, 2024
Gradient-free optimizers allow for tackling problems regardless of the smoothness or differentiability of their objective function, but they require many more iterations to converge when compared to gradient-based algorithms. This has made them unviable for topology optimization due to the high computational cost per iteration and high dimensionality of these problems. We propose a pre-trained neural reparameterization strategy that leads to at least one order of magnitude decrease in iteration count when optimizing the designs in latent space, as opposed to the conventional approach without latent reparameterization. We demonstrate this via extensive computational experiments in- and out-of-distribution with the training data. Although gradient-based topology optimization is still more efficient for differentiable problems, such as compliance optimization of structures, we believe this work will open up a new path for problems where gradient information is not readily available (e.g. fracture).
Continual learning for surface defect segmentation by subnetwork creation and selection
Dec 08, 2023We introduce a new continual (or lifelong) learning algorithm called LDA-CP&S that performs segmentation tasks without undergoing catastrophic forgetting. The method is applied to two different surface defect segmentation problems that are learned incrementally, i.e. providing data about one type of defect at a time, while still being capable of predicting every defect that was seen previously. Our method creates a defect-related subnetwork for each defect type via iterative pruning and trains a classifier based on linear discriminant analysis (LDA). At the inference stage, we first predict the defect type with LDA and then predict the surface defects using the selected subnetwork. We compare our method with other continual learning methods showing a significant improvement -- mean Intersection over Union better by a factor of two when compared to existing methods on both datasets. Importantly, our approach shows comparable results with joint training when all the training data (all defects) are seen simultaneously
iPINNs: Incremental learning for Physics-informed neural networks
Apr 10, 2023
Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and non-unique due to the complexity of the loss landscape that needs to be traversed. Although a variety of multi-task learning and transfer learning approaches have been proposed to overcome these issues, there is no incremental training procedure for PINNs that can effectively mitigate such training challenges. We propose incremental PINNs (iPINNs) that can learn multiple tasks (equations) sequentially without additional parameters for new tasks and improve performance for every equation in the sequence. Our approach learns multiple PDEs starting from the simplest one by creating its own subnetwork for each PDE and allowing each subnetwork to overlap with previously learned subnetworks. We demonstrate that previous subnetworks are a good initialization for a new equation if PDEs share similarities. We also show that iPINNs achieve lower prediction error than regular PINNs for two different scenarios: (1) learning a family of equations (e.g., 1-D convection PDE); and (2) learning PDEs resulting from a combination of processes (e.g., 1-D reaction-diffusion PDE). The ability to learn all problems with a single network together with learning more complex PDEs with better generalization than regular PINNs will open new avenues in this field.
Cooperative data-driven modeling
Nov 23, 2022
Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening possibilities for cooperative modeling. However, artificial neural networks suffer from catastrophic forgetting, i.e. they forget how to perform an old task when trained on a new one. This hinders cooperation because adapting an existing model for a new task affects the performance on a previous task trained by someone else. The authors developed a continual learning method that addresses this issue, applying it here for the first time to solid mechanics. In particular, the method is applied to recurrent neural networks to predict history-dependent plasticity behavior, although it can be used on any other architecture (feedforward, convolutional, etc.) and to predict other phenomena. This work intends to spawn future developments on continual learning that will foster cooperative strategies among the mechanics community to solve increasingly challenging problems. We show that the chosen continual learning strategy can sequentially learn several constitutive laws without forgetting them, using less data to achieve the same error as standard training of one law per model.
Continual Prune-and-Select: Class-incremental learning with specialized subnetworks
Aug 09, 2022
The human brain is capable of learning tasks sequentially mostly without forgetting. However, deep neural networks (DNNs) suffer from catastrophic forgetting when learning one task after another. We address this challenge considering a class-incremental learning scenario where the DNN sees test data without knowing the task from which this data originates. During training, Continual-Prune-and-Select (CP&S) finds a subnetwork within the DNN that is responsible for solving a given task. Then, during inference, CP&S selects the correct subnetwork to make predictions for that task. A new task is learned by training available neuronal connections of the DNN (previously untrained) to create a new subnetwork by pruning, which can include previously trained connections belonging to other subnetwork(s) because it does not update shared connections. This enables to eliminate catastrophic forgetting by creating specialized regions in the DNN that do not conflict with each other while still allowing knowledge transfer across them. The CP&S strategy is implemented with different subnetwork selection strategies, revealing superior performance to state-of-the-art continual learning methods tested on various datasets (CIFAR-100, CUB-200-2011, ImageNet-100 and ImageNet-1000). In particular, CP&S is capable of sequentially learning 10 tasks from ImageNet-1000 keeping an accuracy around 94% with negligible forgetting, a first-of-its-kind result in class-incremental learning. To the best of the authors' knowledge, this represents an improvement in accuracy above 20% when compared to the best alternative method.
Adaptive Clustering-based Reduced-Order Modeling Framework: Fast and accurate modeling of localized history-dependent phenomena
Sep 24, 2021
This paper proposes a novel Adaptive Clustering-based Reduced-Order Modeling (ACROM) framework to significantly improve and extend the recent family of clustering-based reduced-order models (CROMs). This adaptive framework enables the clustering-based domain decomposition to evolve dynamically throughout the problem solution, ensuring optimum refinement in regions where the relevant fields present steeper gradients. It offers a new route to fast and accurate material modeling of history-dependent nonlinear problems involving highly localized plasticity and damage phenomena. The overall approach is composed of three main building blocks: target clusters selection criterion, adaptive cluster analysis, and computation of cluster interaction tensors. In addition, an adaptive clustering solution rewinding procedure and a dynamic adaptivity split factor strategy are suggested to further enhance the adaptive process. The coined Adaptive Self-Consistent Clustering Analysis (ASCA) is shown to perform better than its static counterpart when capturing the multi-scale elasto-plastic behavior of a particle-matrix composite and predicting the associated fracture and toughness. Given the encouraging results shown in this paper, the ACROM framework sets the stage and opens new avenues to explore adaptivity in the context of CROMs.
Neural network relief: a pruning algorithm based on neural activity
Sep 22, 2021
Current deep neural networks (DNNs) are overparameterized and use most of their neuronal connections during inference for each task. The human brain, however, developed specialized regions for different tasks and performs inference with a small fraction of its neuronal connections. We propose an iterative pruning strategy introducing a simple importance-score metric that deactivates unimportant connections, tackling overparameterization in DNNs and modulating the firing patterns. The aim is to find the smallest number of connections that is still capable of solving a given task with comparable accuracy, i.e. a simpler subnetwork. We achieve comparable performance for LeNet architectures on MNIST, and significantly higher parameter compression than state-of-the-art algorithms for VGG and ResNet architectures on CIFAR-10/100 and Tiny-ImageNet. Our approach also performs well for the two different optimizers considered -- Adam and SGD. The algorithm is not designed to minimize FLOPs when considering current hardware and software implementations, although it performs reasonably when compared to the state of the art.
Spiderweb nanomechanical resonators via Bayesian optimization: inspired by nature and guided by machine learning
Aug 10, 2021
From ultra-sensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes which are isolated from ambient thermal environments via a novel "torsional soft-clamping" mechanism discovered by the data-driven optimization algorithm. This bio-inspired resonator is then fabricated; experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design which does not require sub-micron lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. Here we demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.