Neural networks simplify uncertainty quantification of locally nonlinear systems.
problem Estimating statistics of responses in large-scale locally nonlinear dynamical systems.
method Decomposes response into nominal linear system and a neural network-estimated pseudoforce.
result Neural networks can efficiently estimate pseudoforce containing nonlinear and uncertain information.
New framework for managing medical risks using convex responses.
problem Medical risk management and dosing optimization.
method Analyzes convex and concave dose-response functions, defines antifragility.
result Proposes a mathematical framework for integrating nonlinearities in oncology.
CAG method predicts nonlinear solid mechanics responses in real-time with high accuracy and efficiency.
problem Real-time prediction of nonlinear solid mechanics responses.
method Clustering adaptive Gaussian process regression (CAG) method.
result Offers predictions within a second with high precision using only 20 samples.
Incorporating nonlinearity is paramount to predicting the future states of a dynamical system, its response to shocks, and its underlying causal network. However, most existing methods for causality detection and impulse response, such as Vector Autoregression (VAR), assume linearity and are thus unable to capture the …
Framework predicts nonlinear system responses using GFDT and generative models.
problem Predicting higher-order moments of nonlinear stochastic systems to small perturbations.
method Combining GFDT with generative modeling to estimate score function directly from data.
result Accurately captures nonlinear and non-Gaussian features of system responses.
A hybrid method combines model-based and data-driven approaches for multiscale constitutive responses.
problem High computational costs and inaccuracies in nonlinear multiscale methods.
method Hybrid methodology combining model-based constitutive laws, data-driven corrections, and computational multiscale approaches.
result Model-data-driven approach improves macroscale simulations with similar accuracy and computational cost.
We simplify complex regression coefficients using linearization and feature comparison.
problem Interpreting high-dimensional regression coefficients from nonlinear responses.
method Developed a linearization method to derive feature coefficients and compare them with regression coefficients.
result Shows how regression coefficients relate to linearized feature coefficients and how they change under regularization.
DynNet models dynamic responses of linear and nonlinear systems with fewer variables and higher accuracy.
problem Predicting dynamic responses of linear and nonlinear systems.
method Physics-based recurrent neural network with optimized architecture and training techniques.
result Higher accuracy and fewer trainable variables compared to existing models.
Extends RRR to capture nonlinear interactions in multi-response regression.
problem Complex relationships in real-world data cannot be adequately modeled by linear interactions.
method Introduces Higher Order Reduced Rank Regression (HORRR) using tensor representations and Tucker decomposition.
result HORRR can capture nonlinear interactions in multi-response regression.
The study reveals asymmetries in US financial shocks' international impacts.
problem Analyzing nonlinearities in international financial spillovers.
method Developed a flexible nonlinear multi-country model to capture asymmetries in responses to financial shocks.
result Adverse shocks trigger stronger declines in output, inflation, and stock markets than benign shocks.
BART is extended to handle various response variables.
problem Modeling nonlinear regression functions for diverse response types.
method Generalized Bayesian Additive Regression Trees (GBART) for exponential family distributions.
result The posterior concentrates at a minimax rate for certain response distributions.
New algorithms achieve decision calibration without sample complexity dependent on feature dimension.
problem Achieving decision calibration for nonlinear loss functions with polynomial sample complexity.
method Developed smooth relaxation of decision calibration, enabling dimension-free algorithms.
result Efficient algorithms post-process predictors to satisfy decision calibration without worsening accuracy.
Study uses machine learning to predict nonlinear seismic brace behavior.
problem Predicting nonlinear seismic response of structural braces.
method State-of-the-art machine learning techniques, specifically LSTM, were used.
result LSTM method effectively captures nonlinear brace behavior.
New algorithm speeds up IRT model fitting for large datasets.
problem Inefficient algorithms for fitting Item Response Theory models to large datasets.
method Stochastic Variational Inference for IRT models.
result Higher log likelihoods and accuracy in imputing missing data.
Paper generalizes Hardy-Rogers maps for market equilibrium analysis in duopoly markets.
problem Existence and uniqueness of market equilibrium in duopoly markets with non-differentiable, nonlinear response functions.
method Coupled fixed points approach for generalized Hardy-Rogers maps.
result Enriched understanding of market equilibrium in duopoly markets with non-differentiable response functions.
MSRL learns a representation maximizing mutual info with response variables.
problem Learning sufficient representations for complex, multi-dimensional data.
method Variational mutual information, deep neural networks, generalized Dudley's inequality.
result MSRL achieves consistent and accurate representation learning.
An empirical study of joint bivariate probability distribution of two consecutive price increments for a set of stocks at time scales ranging from one minute to thirty minutes reveals asymmetric structures with respect to the axes y=0, y=x, x=0 and y=-x. All four asymmetry patterns remarkably resemble a four-blade mill…
Proposes estimators for complex dose-response curves using kernel methods.
problem Estimating complex dose-response curves with continuous treatments, mediators, and covariates.
method Kernel ridge regression with sequential kernel embedding technique.
result Simple estimators for mediated and time-varying dose response curves with nonasymptotic uniform rates.
In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of p basis functions. We reconstruct the p…
Our objective is to estimate the unknown compositional input from its output response through an unknown system after estimating the inverse of the original system with a training set. The proposed methods using artificial neural networks (ANNs) can compete with the optimal bounds for linear systems, where convex optim…
A central challenge in neuroscience is to understand neural computations and circuit mechanisms that underlie the encoding of ethologically relevant, natural stimuli. In multilayered neural circuits, nonlinear processes such as synaptic transmission and spiking dynamics present a significant obstacle to the creation of…
New method selects direct causal parents from large sets of variables.
problem Inferring direct causal parents from many variables, especially nonlinear and cyclic.
method One-vs.-the-rest feature selection approach with theoretical guarantees.
result Significant improvements over existing methods.
Unified method learns latent spaces from labeled data.
problem Identifying low-dimensional latent structures in high-dimensional data.
method Nonlinear multiple-response regression within an index model context.
result Unified method offers better interpretability and reduced computational complexity.
Novel F2NARX model improves surrogate modeling for stochastic dynamical systems.
problem Challenges in constructing accurate and efficient surrogate models for stochastic dynamical systems.
method Function-on-Function Nonlinear AutoRegressive model with eXogenous inputs (F2NARX) combining PCA and Gaussian process regression.
result F2NARX outperforms state-of-the-art NARX models in efficiency and accuracy.
The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear parabolic partial differential equation for the optimal response function. We construct…
Proposes a partially linear structure to capture nonlinear relationships in mixture of experts models.
problem Suboptimal estimates due to linearity assumption in mixture of experts models.
method Introduces a partially linear structure that incorporates unspecified functions to capture nonlinear relationships.
result Establishes the identifiability of the proposed model under mild conditions and introduces a practical estimation algorithm.
The paper develops exact and approximate conformal inference methods for multi-output regression.
problem Uncertainty quantification in multi-output regression predictions.
method Exact derivations and approximations of conformal inference p-values for linear multi-output predictors, and efficient methods for nonlinear predictors.
result Efficient methods for approximating conformal prediction regions for multi-output predictors, both linear and nonlinear.
New model uses symmetries and scaling laws to predict consumer advertising response.
problem Understanding consumer response to advertising efforts.
method Introduces a physics-based mathematical model to describe consumer response dynamics.
result The model better captures nonlinearities in advertising effects and provides new parameters for audience engagement.
Here, we present a novel approach to solve the problem of reconstructing perceived stimuli from brain responses by combining probabilistic inference with deep learning. Our approach first inverts the linear transformation from latent features to brain responses with maximum a posteriori estimation and then inverts the …
A nonlinear channel estimator using complex Least Square Support Vector Machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long Term Evolution (LTE) downlink under high mobility conditions. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the …
This paper presents a new method for solving systems with polynomial stiffness.
problem Finding analytical solutions to nonlinear differential equations with polynomial stiffness is challenging.
method The paper introduces a geometric/algebraic method using generating series and shuffle product.
result The method provides a recursive schematic that can be automated and applied to systems with polynomial stiffness.
In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two objectives at the same time: to accurately predict dynamics of complex systems and to …
New kernel methods estimate complex causal relationships.
problem Estimating nonparametric causal functions like dose-response curves.
method Kernel ridge regression with decomposition property.
result Uniform consistency with finite sample rates proved.
A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, with…
We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we construct a deep convolutional neural network in which the parameters are used to cl…
Improves regression efficiency by separating material and immaterial parts of responses.
problem Improving estimation efficiency in nonlinear multivariate regressions.
method Kernel envelope (KENV) estimator for nonparametric response envelopes in reproducing kernel Hilbert space.
result KENV achieves lower in-sample prediction risk than kernel ridge regression in non-trivial immaterial components.
The paper introduces neural INGARCH models for time series of counts.
problem Analyzing time series of counts using traditional INGARCH models.
method Combining artificial neural networks with INGARCH models.
result Neural INGARCH models outperform traditional models in information loss.
Surrogate models help predict complex systems with less computational cost.
problem Uncertainty in complex systems due to variability and external loads.
method Surrogate models trained on limited simulations to approximate full time-dependent response.
result Efficient surrogate models reduce computational expense for UQ in nonlinear dynamics.
New geometric theory explains nonuniform origami responses.
problem Understanding nonuniform responses in origami sheets.
method Purely geometric continuum theory capturing nonuniform, nonlinear response.
result Three modes govern nonuniform response, varying smoothly across the sheet.
New method for reducing dimensions of distributional data.
problem Nonlinear sufficient dimension reduction for distribution-on-distribution regression.
method Building universal kernels on metric spaces to characterize conditional independence.
result Method outperforms competing methods in synthetic and real data applications.
Neural network predicts functional responses from scalar inputs.
problem Regression of functional responses with large scalar predictors and nonlinear relationships.
method Transform functional response to finite dimensions, design feed-forward neural network, modify output via objective functions, apply roughness penalty.
result Proposed neural network outperforms conventional methods in multiple scenarios.
Enhances RSCNs with hybrid regularization for nonlinear dynamics.
problem Modeling nonlinear dynamic systems with uncertainties.
method Recurrent stochastic configuration networks with hybrid regularization.
result The method outperforms other models in nonlinear system identification and industrial tasks.
New method calculates sensitivity of system failure probability.
problem Difficulty in computing sensitivity of failure probability.
method Monte Carlo strategy using response gradient and kernel smoothing.
result Single Monte Carlo run for sensitivity estimates.
Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.
problem Learning nonlinear factor models with unknown monotone links from incomplete and noisy data.
method Formulated as joint recovery of low-rank factors, loadings, and nonlinear link function; proposed BCD algorithm with regularization.
result Established convergence guarantees and sublinear regret bounds for link-function updates.
A hybrid ML method improves ship response predictions across different sea conditions.
problem Improving accuracy and generalizability of ML methods for ship response predictions.
method A hybrid machine learning method that corrects forces in a low-fidelity equation of motion.
result The hybrid method offers improved prediction accuracy and generalizability compared to benchmarks.
This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or tertiary predictors and allows the number of predictors to exceed the size of the sa…
Characterizes Hessian eigenspectra for realistic nonlinear models.
problem Understanding Hessian eigenspectra in realistic nonlinear models.
method Deterministic equivalent techniques from random matrix theory.
result Hessian can have qualitatively different spectral behaviors.
Functional PLS improves prediction and inference for scalar responses from functional predictors.
problem Estimating scalar responses from functional predictors in an ill-posed inverse problem.
method Functional partial least squares (PLS) estimator with adaptive early stopping and new tests.
result PLS attains nearly minimax-optimal convergence rates and detects local alternatives.