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Characterizing Risk Regimes for Safe Deployment of Deep Regression Models
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PAGER: A Framework for Failure Analysis of Deep Regression Models
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IRNet: A General Purpose Deep Risidual Regression Framework for Materials Discovery
Materials discovery is crucial for making scientific advances in many domains. Collections of data from experiments and first-principle computations have spurred interest in applying machine learning methods to create predictive models capable of mapping from composition and crystal structures to materials properties. Generally, these are regression problems with the input being a 1D vector composed of numerical attributes representing the material composition and/or crystal structure. While neural networks consisting of fully connected layers have been applied to such problems, their performance often suffers from the vanishing gradient problem when network depth is increased. Hence, predictive modeling for such tasks has been mainly limited to traditional machine learning techniques such as Random Forest. In this paper, we study and propose design principles for building deep regression networks composed of fully connected layers with numerical vectors as input. We introduce a novel deep regression network with individual residual learning, IRNet, that places shortcut connections after each layer so that each layer learns the residual mapping between its output and input. We use the problem of learning properties of inorganic materials from numerical attributes derived from material composition and/or crystal structure to compare IRNet’s performance against that of other machine learning techniques. Using multiple datasets from the Open Quantum Materials Database (OQMD) and Materials Project for training and evaluation, we show that IRNet provides significantly better prediction performance than the state-of-the-art machine learning approaches currently used by domain scientists. We also show that IRNet’s use of individual residual learning leads to better convergence during the training phase than when shortcut connections are between multi-layer stacks while maintaining the same number of parameters.
Deep Symbolic Regression
Symbolic regression is the task of finding tractable mathematical expressions that best fit an input dataset. Deep symbolic regression (DSR) searches the space of tractable mathematical expressions by using a recurrent neural network that generates mathematical expressions. The network is trained using reinforcement learning.
Nanosecond machine learning regression with deep boosted decision trees in FPGA for high energy physics
We present a novel application of the machine learning / artificial intelligence method called boosted decision trees to estimate physical quantities on field programmable gate arrays (FPGA). The software package fwXmachina features a new architecture called parallel decision paths that allows for deep decision trees with arbitrary number of input variables. It also features a new optimization scheme to use different numbers of bits for each input variable, which produces optimal physics results and ultraefficient FPGA resource utilization. Problems in high energy physics of proton collisions at the Large Hadron Collider (LHC) are considered. Estimation of missing transverse momentum (E T miss ) at the first level trigger system at the High Luminosity LHC (HL-LHC) experiments, with a simplified detector modeled by Delphes, is used to benchmark and characterize the firmware performance. The firmware implementation with a maximum depth of up to 10 using eight input variables of 16-bit precision gives a latency value of $\mathcal{O}$(10) ns, independent of the clock speed, and $\mathcal{O}$(0.1)% of the available FPGA resources without using digital signal processors.
A demonstration platform for deep symbolic regression
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Deep Symbolic Regression
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Symbolic Regression via Deep Reinforcement Learning Enhanced Genetic Programming Seeding.
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Revisit the Scalability of Deep Auto-Regressive Models for Graph Generation
As a new promising approach to graph generations, deep auto-regressive graph generation has drawn increasing attention. It however has been commonly deemed as hard to scale up to work with large graphs. In existing studies, it is perceived that the consideration of the full non-local graph dependences is indispensable for this approach to work, which entails the needs for keeping the entire graph’s info in memory and hence the perceived “inherent” scalability limitation of the approach. This paper revisits the common perception. It proposes three ways to relax the dependences and conducts a series of empirical measurements. It concludes that the perceived “inherent” scalability limitation is a misperception; with the right design and implementation, deep auto-regressive graph generation can be applied to graphs much larger than the device memory. The rectified perception removes a fundamental barrier for this approach to meet practical needs.
Deep energy-pressure regression for a thermodynamically consistent EOS model
Abstract In this paper, we aim to explore novel machine learning (ML) techniques to facilitate and accelerate the construction of universal equation-Of-State (EOS) models with a high accuracy while ensuring important thermodynamic consistency. When applying ML to fit a universal EOS model, there are two key requirements: (1) a high prediction accuracy to ensure precise estimation of relevant physics properties and (2) physical interpretability to support important physics-related downstream applications. We first identify a set of fundamental challenges from the accuracy perspective, including an extremely wide range of input/output space and highly sparse training data. We demonstrate that while a neural network (NN) model may fit the EOS data well, the black-box nature makes it difficult to provide physically interpretable results, leading to weak accountability of prediction results outside the training range and lack of guarantee to meet important thermodynamic consistency constraints. To this end, we propose a principled deep regression model that can be trained following a meta-learning style to predict the desired quantities with a high accuracy using scarce training data. We further introduce a uniquely designed kernel-based regularizer for accurate uncertainty quantification. An ensemble technique is leveraged to battle model overfitting with improved prediction stability. Auto-differentiation is conducted to verify that necessary thermodynamic consistency conditions are maintained. Our evaluation results show an excellent fit of the EOS table and the predicted values are ready to use for important physics-related tasks.
Multilevel-in-width training for deep neural network regression
A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible solutions so as to discourage overfitting while still enabling good solutions, and different regularization strategies impose different types of restrictions. In this paper, we present a multilevel regularization strategy that constructs and trains a hierarchy of neural networks, each of which has layers that are wider versions of the previous network's layers. Here, we draw intuition and techniques from the field of Algebraic Multigrid (AMG), traditionally used for solving linear and nonlinear systems of equations, and specifically adapt the Full Approximation Scheme (FAS) for nonlinear systems of equations to the problem of deep learning. Training through V-cycles then encourage the neural networks to build a hierarchical understanding of the problem. We refer to this approach as multilevel-in-width to distinguish from prior multilevel works which hierarchically alter the depth of neural networks. The resulting approach is a highly flexible framework that can be applied to a variety of layer types, which we demonstrate with both fully connected and convolutional layers. We experimentally show with PDE regression problems that our multilevel training approach is an effective regularizer, improving the generalize performance of the neural networks studied.
Deep Neural Network Algorithm for CMC Microstructure Characterization and Variability Quantification
Microstructure characterization and variability quantification are crucial for understanding ceramic matrix composites (CMCs) mechanical behavior and deformation mechanisms across length scales. Traditionally, analyses of the micrographs obtained from microscopy are labor-intensive. However, with the vast improvement in computer vision (CV) and deep learning (DL), an automated algorithm can be designed to extract essential microstructure variability from micrographs which can then be used to construct a statistically representative volume element (SRVE). The DL-based algorithm spans the taxonomy of microstructure analyses, including semantic segmentation of microstructure constituents, secondary phases, matrix/fiber interface, and defects, and quantifying the microstructure variability in terms of probability distributions. In this work, C/SiNC and SiC/SiNC CMCs microstructures are semantically segmented through a deep convolutional neural network, followed by variability quantification through the implementation of a fully connected regression layer, hence forming a deep regression network. The deep regression network operates in a feedforward regime, in which the neuron output signal traverses through the network in a unidirectional manner. The weight tensor associated with each layer is updated through a backpropagation stochastic gradient descent approach. The input gray-scale image obtained through in-house scanning electron microscope and confocal microscope micrographs is augmented through affine transformations to increase the training set size, which is then processed through four strided convolutional layers. This compresses the image resolution by half at each layer while increasing the image depth by applying different filters (image encoding). The class activation maps (CAMs) corresponding to the applied filters highlight the key architectural features and assist with the semantic segmentation of the microstructure.
Computer Model Calibration with Time Series Data Using Deep Learning and Quantile Regression
Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiments is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data, such as large time series, due to the difficulty in building an emulator and the nonidentifiability between effects from input parameters and data-model discrepancy. To overcome these challenges, we, in this work, propose a new calibration framework based on a deep neural network (DNN) with long short-term memory layers that directly emulates the inverse relationship between the model output and input parameters. Adopting the “learning with noise” idea, we train our DNN model to filter out the effects from data-model discrepancy on input parameter inference. We also formulate a new way to construct interval predictions for DNN using quantile regression to quantify the uncertainty in input parameter estimates. Through a simulation study and real data application with the Weather Research and Forecasting Model Hydrological modeling system (WRF-Hydro), we show our approach can yield accurate point estimates and well-calibrated interval estimates for input parameters.
Adaptive Activation Functions Accelerate Convergence in Deep and Physics-informed Neural Networks
We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In particular, we solve the nonlinear Klein-Gordon equation, which has smooth solutions, the nonlinear Burgers equation, which can admit high gradient solutions, and the Helmholtz equation. We introduce a scalable hyper-parameter in the activation function, which can be optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The adaptive activation function has better learning capabilities than the traditional one (fixed activation) as it improves greatly the convergence rate, especially at early training, as well as the solution accuracy. To better understand the learning process, we plot the neural network solution in the frequency domain to examine how the network captures successively different frequency bands present in the solution. We consider both forward problems, where the approximate solutions are obtained, as well as inverse problems, where parameters involved in the governing equation are identified. Our simulation results show that the proposed method is a very simple and effective approach to increase the efficiency, robustness and accuracy of the neural network approximation of nonlinear functions as well as solutions of partial differential equations, especially for forward problems. We theoretically prove that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima.
Hypothesis testing via AI: Generating physically interpretable models of scientific data with machine learning (Full Technical Report)
Deep learning has demonstrated an exceptional ability to solve complex tasks (an engineering success); however, it has done so at the expense of the ability to generate new knowledge (a scientific failure). We propose an alternative framework—entitled Deep Symbolic Regression (DSR)—in which artificial neural networks (NNs) rapidly generate hypotheses about physical relationships among inputs. This framework bypasses the need to interpret an NN altogether, while still leveraging the representational power of deep learning. The resulting models are tractable mathematical expressions, which are inherently and readily human interpretable and can provide insights into underlying physical phenomena. Further, we fold this methodology into the scientific process by allowing the scientist to directly integrate a priori knowledge and beliefs to accelerate learning. We demonstrate this methodology on symbolic regression—the problem of rediscovering underlying expressions describing a dataset—and achieve state-of-the-art performance across a wide variety of symbolic regression problems. Further, we generalize our DSR framework to apply to the more general class of symbolic optimization problems, in which one seeks to optimize a sequence of symbols or “tokens” under a black-box reward function. Examples of other symbolic optimization problems include neural architecture search and computational antibody design. Our generalized tool, Deep Symbolic Optimization (DSO), has been demonstrated on the task of learning symbolic control policies for reinforcement learning environments, and has been adopted as an enabling capability for computational antibody design.
Optimizing transmit field inhomogeneity of parallel RF transmit design in 7T MRI using deep learning
Ultrahigh field (UHF) Magnetic Resonance Imaging (MRI) provides a higher signal-to-noise ratio and, thereby, higher spatial resolution. However, UHF MRI introduces challenges such as transmit radiofrequency (RF) field (B+1) inhomogeneities, leading to uneven flip angles and image intensity anomalies. These issues can significantly degrade imaging quality and its medical applications. This study addresses B+1 field homogeneity through a novel deep learning-based strategy. Traditional methods like Magnitude Least Squares (MLS) optimization have been effective but are time-consuming and dependent on the patient’s presence. Recent machine learning approaches, such as RF Shim Prediction by Iteratively Projected Ridge Regression and deep learning frameworks, have shown promise but face limitations like extensive training times and oversimplified architectures. We propose a two-step deep learning strategy. First, we obtain the desired reference RF shimming weights from multi-channel B+1 fields using random-initialized Adaptive Moment Estimation. Then, we employ Residual Networks (ResNets) to train a model that maps B+1 fields to target RF shimming outputs. Our approach does not rely on pre-calculated reference optimizations for the testing process and efficiently learns residual functions. Comparative studies with traditional MLS optimization demonstrate our method’s advantages in terms of speed and accuracy. The proposed strategy achieves a faster and more efficient RF shimming design, significantly improving imaging quality at UHF. This advancement holds potential for broader applications in medical imaging and diagnostics.
Accelerating the discovery of battery electrode materials through data mining and deep learning models
The availability of crystalline materials databases allows for building accurate machine learning (ML) models that can accelerate the exploration of materials chemical space for energy storage applications. In this work, we screen all inorganic materials included in the Materials Project and AFLOW databases as potential metal-ion battery electrodes. We develop an efficient protocol to mine and screen raw data in current databases and provide a new database of electrode materials by considering pairs of charged and discharged electrodes. This effort leads to a new database with over 190,000 instances, in contrast to the original battery database which contains about 5000. The expanded battery data set is then used to build regression-based deep neural network models for predicting average voltages and percentage volume changes upon charging and discharging, which present improvements of at least 28% for target properties with respect to previous models, and are now able to predict anode electrodes (low voltage region) as well as electrodes that will not work in electrochemical cells (negative voltages), overcoming the challenges identified in previous ML models for battery electrodes. Additionally, a further screening of the expanded database itself allowed us to identify 35 novel electrode candidates with excellent battery performance metrics.