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Found 46 papers, 8 papers with code
Nonlinear Manifold Learning Determines Microgel Size from Raman Spectroscopy
Polymer particle size constitutes a crucial characteristic of product quality in polymerization.
Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks
We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem.
Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification
To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data.
AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression
The performance of this framework is validated by recovering the right-hand sides and unknown terms of certain complex, chaotic systems such as the well-known Lorenz system, a six-dimensional hyperchaotic system, and the non-autonomous Sprott chaotic system, and comparing them with their known analytical expressions.
Gappy local conformal auto-encoders for heterogeneous data fusion: in praise of rigidity
Fusing measurements from multiple, heterogeneous, partial sources, observing a common object or process, poses challenges due to the increasing availability of numbers and types of sensors.
Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems
A valuable step in the modeling of multiscale dynamical systems in fields such as computational chemistry, biology, materials science and more, is the representative sampling of the phase space over long timescales of interest; this task is not, however, without challenges.
Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling
We study the tipping point collective dynamics of an adaptive susceptible-infected-susceptible (SIS) epidemiological network in a data-driven, machine learning-assisted manner.
Machine Learning for the identification of phase-transitions in interacting agent-based systems
Deriving closed-form, analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs).
Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML era
Both Black-Box and (theoretically-informed and data-corrected) Gray-Box models are described; the necessity for the latter arises when truncated Galerkin projections are so inaccurate as to not be amenable to post-processing.
Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points
We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipping points in the emergent behavior of complex systems, and (b) characterizing probabilities of rare events (here, catastrophic shifts) near them.
Data-driven and Physics Informed Modelling of Chinese Hamster Ovary Cell Bioreactors
Fed-batch culture is an established operation mode for the production of biologics using mammalian cell cultures.
Some of the variables, some of the parameters, some of the times, with some physics known: Identification with partial information
Iterates of such neural-network models allow for learning from data sampled at arbitrary time points $\textit{without}$ data modification.
Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets
We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss.
Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learning
We assess the performance of the proposed PIML approach via a benchmark nonlinear discrete map for which the feedback linearization transformation law can be derived analytically; the example is characterized by steep gradients, due to the presence of singularities, in the domain of interest.
On Equivalent Optimization of Machine Learning Methods
Our data-driven approach is general and can be utilized broadly to compare the optimization of machine learning methods.
Gentlest ascent dynamics on manifolds defined by adaptively sampled point-clouds
Finding saddle points of dynamical systems is an important problem in practical applications such as the study of rare events of molecular systems.
Certified Invertibility in Neural Networks via Mixed-Integer Programming
Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network's output.
A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms
Meta-learning of numerical algorithms for a given task consists of the data-driven identification and adaptation of an algorithmic structure and the associated hyperparameters.
Data-driven Discovery of Chemotactic Migration of Bacteria via Machine Learning
The resulting data-driven PDE can then be simulated to reproduce/predict computational or experimental bacterial density profile data, and estimate the underlying (unmeasured) chemonutrient field evolution.
Limits of Entrainment of Circadian Neuronal Networks
In this work, we study a modern computational neuroscience model to determine the limits of circadian synchronization to external light signals of different frequency and duty cycle.
GANs and Closures: Micro-Macro Consistency in Multiscale Modeling
In this work, we present an approach that couples physics-based simulations and biasing methods for sampling conditional distributions with ML-based conditional generative adversarial networks for the same task.
Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach
We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems modelled via microscopic/agent-based simulators.
Black and Gray Box Learning of Amplitude Equations: Application to Phase Field Systems
In these regimes, going beyond black-box identification, we explore different approaches to learn data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations.
Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data
We exploit Automatic Relevance Determination (ARD) within a Gaussian Process framework for the identification of a parsimonious set of collective observables that parametrize the law of the effective PDEs.
Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles
We construct a reduced, data-driven, parameter dependent effective Stochastic Differential Equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian Dynamics Simulations.
Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space
A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models.
Staying the course: Locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds
As in the Euclidean case, generalized isoclines of generic vector fields $X$ are smooth curves that connect equilibria of $X$.
Weakly Supervised Indoor Localization via Manifold Matching
Inferring the location of a mobile device in an indoor setting is an open problem of utmost significance.
An Operator Theoretic View on Pruning Deep Neural Networks
The discovery of sparse subnetworks that are able to perform as well as full models has found broad applied and theoretical interest.
On the Parameter Combinations That Matter and on Those That do Not
We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models.
On the Correspondence between Gaussian Processes and Geometric Harmonics
We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts.
Learning the temporal evolution of multivariate densities via normalizing flows
Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time.
Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics.
Personalized Algorithm Generation: A Case Study in Learning ODE Integrators
As a case study, we develop a machine learning approach that automatically learns effective solvers for initial value problems in the form of ordinary differential equations (ODEs), based on the Runge-Kutta (RK) integrator architecture.
Initializing LSTM internal states via manifold learning
We present an approach, based on learning an intrinsic data manifold, for the initialization of the internal state values of LSTM recurrent neural networks, ensuring consistency with the initial observed input data.
Helmholtzian Eigenmap: Topological feature discovery & edge flow learning from point cloud data
In this work, we propose the estimation of the manifold Helmholtzian from point cloud data by a weighted 1-Laplacian $\mathcal L_1$.
Learning emergent PDEs in a learned emergent space
These coordinates then serve as an emergent space in which to learn predictive models in the form of partial differential equations (PDEs) for the collective description of the coupled-agent system.
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data.
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
Training deep neural networks to learn such data-driven partial differential operators requires extensive spatiotemporal data.
Numerical Analysis Numerical Analysis Computational Physics 35B27
Transformations between deep neural networks
We propose to test, and when possible establish, an equivalence between two different artificial neural networks by attempting to construct a data-driven transformation between them, using manifold-learning techniques.
LOCA: LOcal Conformal Autoencoder for standardized data coordinates
We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, non-linear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized latent variables.
Spectral Discovery of Jointly Smooth Features for Multimodal Data
We show analytically that our method is guaranteed to provide a set of orthogonal functions that are as jointly smooth as possible, ordered by increasing Dirichlet energy from the smoothest to the least smooth.
Coarse-scale PDEs from fine-scale observations via machine learning
In this paper, we introduce a data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine learning algorithms.
Domain Adaptation with Optimal Transport on the Manifold of SPD matrices
We model the difference between two domains by a diffeomorphism and use the polar factorization theorem to claim that OT is indeed optimal for DA in a well-defined sense, up to a volume preserving map.
Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion
In this paper, we will explore mathematical algorithms for multifidelity information fusion that use such an approach towards improving the representation of the high-fidelity function with only a few training data points.
On the sighting of unicorns: a variational approach to computing invariant sets in dynamical systems
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics.
Dynamical Systems Chaotic Dynamics
