Mathematical modeling | Numerical analysis | Design of experiments
A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so a model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (length, curvature, material, ..). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and what-if analysis become impossible since they require thousands or even millions of simulation evaluations. One way of alleviating this burden is by constructing approximation models, known as surrogate models, metamodels or emulators, that mimic the behavior of the simulation model as closely as possible while being computationally cheap(er) to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), solely the input-output behavior is important. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points. This approach is also known as behavioral modeling or black-box modeling, though the terminology is not always consistent. When only a single design variable is involved, the process is known as curve fitting. Though using surrogate models in lieu of experiments and simulations in engineering design is more common, surrogate modeling may be used in many other areas of science where there are expensive experiments and/or function evaluations. (Wikipedia).
Abstract Algebra | Surjective Functions
We give the definition of a surjective function, an outline for proving that a function is surjective, and some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
(ML 13.6) Graphical model for Bayesian linear regression
As an example, we write down the graphical model for Bayesian linear regression. We introduce the "plate notation", and the convention of shading random variables which are being conditioned on.
From playlist Machine Learning
Injective, Surjective and Bijective Functions (continued)
This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.
From playlist Foundational Math
Linear regression is used to compare sets or pairs of numerical data points. We use it to find a correlation between variables.
From playlist Learning medical statistics with python and Jupyter notebooks
The Definition of a Surjective(Onto) Function and Explanation
The Definition of a Surjective(Onto) Function and Explanation
From playlist Functions, Sets, and Relations
21 Spatial Data Analytics: Spatial Scale
Subsurface modeling course lecture on scale.
From playlist Spatial Data Analytics and Modeling
Relevance model 1: Bernoulli sets vs. multinomial urns
[http://bit.ly/RModel] Relevance model is the language model of the relevant class. In this video we look at the difference between the multinomial model (the one used in relevance models) and the multiple-Bernoulli model, which forms the basis for the classical probabilistic models.
From playlist IR18 Relevance Model
Inefficient Feeling: Care as Revolutionary Praxis at the End of Society
Kalindi Vora is Professor of Gender, Sexuality and Women’s Studies at UC Davis, and Director of the Feminist Research Institute. She previously taught at UC San Diego Ethnic Studies and was affiliated with the Science Studies Program. She is author of Life Support: Biocapital and the New H
From playlist Center for the Study of Race, Indigeneity, and Transnational Migration (RITM)
On the Use of (Linear) Surrogate Models for Bayesian Inverse Problems
42nd Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk Date: Wednesday, April 13, 10:00am Eastern Speaker: Ru Nicholson, University of Auckland Abstract: In this talk we consider the use of surrogate (forward) models to efficiently solve Bayesian inverse pr
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
generative model vs discriminative model
understanding difference between generative model and discriminative model with simple example. all machine learning youtube videos from me, https://www.youtube.com/playlist?list=PLVNY1HnUlO26x597OgAN8TCgGTiE-38D6
From playlist Machine Learning
DDPS | Neural architecture search for surrogate modeling
In this talk from May 27th, 2021, Romit Maulik of Argonne National Laboratory discusses recent results from the use of parallelized neural architecture search (NAS) for discovering non-intrusive surrogate models from data. NAS is deployed using DeepHyper, a scalable neural architecture and
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Stefano Marelli: Metamodels for uncertainty quantification and reliability analysis
Abstract: Uncertainty quantification (UQ) in the context of engineering applications aims aims at quantifying the effects of uncertainty in the input parameters of complex models on their output responses. Due to the increased availability of computational power and advanced modelling tech
From playlist Probability and Statistics
DSI | AI-Enabled Innovations in Validation of Sanitation and Detection of Pathogens by Nitin Nitin
Food safety is one of the leading public health issues that continue to be a significant challenge for the food industry and consumers. These issues are critical for the minimally processed food products such as the fresh produce industry. Sanitation is a critical control step for the safe
From playlist DSI Virtual Seminar Series
Yuandong Tian - AI-guided nonlinear optimization for real-world problems - IPAM at UCLA
Recorded 28 February 2023. Yuandong Tian of the Artificial Intelligence Center presents "AI-guided nonlinear optimization for real-world problems" at IPAM's Artificial Intelligence and Discrete Optimization Workshop. Abstract: Efficiently solving real-world optimization problems remains a
From playlist 2023 Artificial Intelligence and Discrete Optimization
Data-driven reconstruction of chaotic dynamics... - Bocquet - Workshop 2 - CEB T3 2019
Bocquet (ENPC, FR) / 14.11.2019 Data-driven reconstruction of chaotic dynamics using data assimilation and machine learning ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/Institu
From playlist 2019 - T3 - The Mathematics of Climate and the Environment
A high level view of reduced order modeling for plasmas
Plasma physics relies on a hierarchy of modeling with successive approximations in order to efficiently simulate plasmas and use real-time control on real-world plasma devices. Here, we provide a high level view of our recent work that attempts to build a bridge between the many magnetohyd
From playlist Research Abstracts from Brunton Lab
CliqueCNN: Self-supervised image representation learning
How to learn useful representation from just a bunch of unlabeled images? I will give a high-level overview of what is self-supervised learning and explain the CliqueCNN method. We will also briefly talk about a bunch of other important self-supervised learning methods Annotations for ev
From playlist Computer Vision
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
DDPS | Efficient nonlinear manifold reduced order model
Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this t
From playlist Data-driven Physical Simulations (DDPS) Seminar Series