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Science-Guided Design and Evaluation of Machine Learning Models: A Case-Study on Multi-Phase Flows
Published in Anuj Karpatne, Ramakrishnan Kannan, Vipin Kumar, Knowledge-Guided Machine Learning, 2023
Nikhil Muralidhar, Jie Bu, Ze Cao, Long He, Naren Ramakrishnan, Danesh Tafti, Anuj Karpatne
The field of knowledge discovery and data mining involves a well-established multi-step pipeline [8, 9] involving unprocessed (raw) data at the outset followed by Data Processing & Transformation→Model Design→Model Training→Inference→Model Decision Evaluation. Prior knowledge about the scientific domain under consideration may be incorporated into this ML pipeline as inductive bias. Note that the use of inductive bias is common in many standard deep learning frameworks such as convolutional neural networks (CNNs) that assumes a special type of spatial structure in the data [25] and also encodes many desirable properties like parameter sharing and translation equivariance [17]. In particular, each step of the ML pipeline may be augmented according to scientific principles known about an application domain of interest being modeled. Figure 9.2 depicts a general SGML pipeline that we detail in this chapter. The pipeline consists of a dataset X, which may be a result of some experiment or scientific simulation.
Regression for Data Analytics
Published in Mohiuddin Ahmed, Al-Sakib Khan Pathan, Data Analytics, 2018
Now we will be calculating the likelihood of our model. Likelihood is one kind of probability where we have the data before calculating probability. We have data y, and we assume it comes from some distribution and the data examples are independent and identically distributed (IID). This means all the examples of data have the same probability distribution as the others and all are mutually independent. Linear regression follows normal distribution. It is an inductive bias of the model. Inductive bias is the assumption that your model takes into account before learning/computation. The total likelihood is the product of the likelihood for each point yi
Deep learning for industrial image: challenges, methods for enriching the sample space and restricting the hypothesis space, and possible issue
Published in International Journal of Computer Integrated Manufacturing, 2022
Tianyuan Liu, Jinsong Bao, Junliang Wang, Jiacheng Wang
Based on knowledge of computational learning theory, features from the industrial image dataset raise the issue that the empirical error of the DLMs can converge to 0, but the difference between the generalization error and the empirical error is relatively large. The characteristics of the industrial image itself will make it difficult for the empirical error of the DLMs to approach 0, and the generalization error is still far from the empirical error. Furthermore, it is known that the characteristic of small sample can lead to insufficient information in the sample space, such that DLMs lack inductive bias. The unbalanced feature of the dataset leads to inductive bias that are far from the actual problem. The characteristics of the industrial image itself will lead to the complexity of the image patterns and therefore require a larger space of hypothesis to find an optimal solution. In addition, the explicit semantic nature contained in industrial image contradicts the unexplainability of DLMs.
Physical Domain Reconstruction with Finite Volume Neural Networks
Published in Applied Artificial Intelligence, 2023
Coşku Can Horuz, Matthias Karlbauer, Timothy Praditia, Martin V. Butz, Sergey Oladyshkin, Wolfgang Nowak, Sebastian Otte
Physics-informed machine learning approaches incorporate physical knowledge as inductive bias (Battaglia et al. 2018). When applied to corresponding physical domains, they yield improvements in generalization and data efficiency when contrasted with pure machine learning (ML) systems (Karlbauer et al. 2021; Raissi, Perdikaris, and Karniadakis 2019). Moreover, inductive biases often help ML models to play down their “technical debt” (Sculley et al. 2015), effectively reducing model complexity while improving model explainability. Several recently proposed approaches augment neural networks with physical knowledge (Le Guen and Thome 2020; Li et al. 2020; Long et al. 2018; Seo, Meng, and Liu 2019; Sitzmann et al. 2020).
Nonparametric Modeling and Prognosis of Condition Monitoring Signals Using Multivariate Gaussian Convolution Processes
Published in Technometrics, 2018
Raed Kontar, Shiyu Zhou, Chaitanya Sankavaram, Xinyu Du, Yilu Zhang
The key feature in multitask learning is to introduce an inductive bias to leverage the commonality among related tasks and capture their intrinsic relatedness to improve prediction and learning accuracy. This inductive transfer is achieved through a shared representation of the training and testing tasks. The key assumption is that tasks share some commonality (Argyriou, Evgeniou, and Pontil 2008; Kumar and Daume 2012; Tseng, Ghosh, and Zhou 2015).