Paper uses autoencoders for efficient reduced-order modeling of eigenvalue problems.
problem Efficiently modeling eigenvalue problems in high dimensions.
method Autoencoder-based reduced-order modeling for eigenvalue problems.
result Autoencoder-based models outperform standard POD-Galerkin methods in neutron diffusion applications.
Develops an importance sampling estimator for complex systems.
problem Estimating the probability of QoI exceeding a threshold in complex systems.
method Coupling reduced-order model and generative model for variance reduction.
result Effective technique to reduce bias and variance in importance sampling.
Paper introduces techniques to learn higher-order programs, improving predictive accuracy and reducing learning times.
problem Expressing and learning complex programs in ILP.
method Extending meta-interpretive learning to support higher-order definitions as background knowledge.
result Learning higher-order programs reduces hypothesis space and sample complexity, improving predictive accuracy and reducing learning times.
This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a distribution over the true error. The variance of this distribution can be…
Paper tackles uncertainties in reduced-order modeling of complex systems.
problem Model-form uncertainties in reduced-order modeling of complex systems.
method Combines Riemannian projection and retraction operators on a subset of the Stiefel manifold with an information-theoretic formulation.
result Identifies and quantifies the impact of model-form uncertainties on inferred operators.
BayPOD-AL learns reduced-order models from high-fidelity data efficiently.
problem Capturing dynamics of complex systems with large training datasets.
method Bayesian active learning based on uncertainty-aware POD.
result BayPOD-AL reduces computational cost and improves model accuracy.
Artificial neural networks infer gravitational-wave parameters from reduced-order waveforms.
problem Efficiently infer gravitational-wave parameters from noisy data.
method Represent waveforms as weighted sums over reduced bases, train neural networks to map source parameters to coefficients.
result Fast and accurate interpolation of gravitational-wave coefficients.
A new method reduces model complexity in DMD using LARS.
problem Building accurate reduced-order models from data.
method Least Angle Regression (LARS) for Dynamic Mode Decomposition (DMD).
result LARS4DMD produces comparable performance to DMDSP with less complexity.
The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly …
New framework quantifies uncertainty in reduced-order models for PDEs.
problem Quantifying reliability of reduced-order model predictions for PDEs.
method Combining stochastic representation of reduced bases with conformal-type methods.
result Provides prediction sets with coordinate miscoverage guarantees.
Study convex embeddability in linear and circular orders, applying to knots.
problem Understanding the quasi-order of convex embeddability in linear and circular orders.
method Combinatorial and descriptive set-theoretic methods applied to arcs and knots.
result Established combinatorial properties and lower bounds for knot complexity.
Novel hybrid modeling combines ML and physics for real-time diagnosis.
problem Real-time diagnosis of complex systems.
method Combines machine learning and physics-based models to create reduced-order models.
result Generated models are two orders of magnitude simpler, improving efficiency.
Develops higher-order Euler-Poincaré field equations for principal G-bundles.
problem Formulating field equations for higher-order jet bundles of principal G-bundles.
method Reduction theory applied to G-invariant Lagrangian field theories on jet bundles, transferring Hamilton's principle to reduced configuration bundles. result Higher-order Euler-Poincaré field equations are equivalent to conservation of Noether current.
New method speeds up deep neural networks inference.
problem Inference speed of deep neural networks.
method Maximum volume algorithm for reduced-order modeling.
result Convolutional layers can be replaced with smaller fully-connected layers with minimal accuracy loss.
Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish tha…
A hybrid model reduces graph complexity for improved classification accuracy.
problem High computational complexity and large number of parameters in higher-order graph convolutional networks.
method Weight sharing mechanism and novel fusion pooling layer to reduce parameters and complexity.
result The proposed model achieves highest classification accuracy with fewer trainable parameters.
ROMs speed up option pricing under stochastic volatility and jump-diffusion models.
problem Efficiently pricing European and American options under complex stochastic models.
method Reduced order modeling using POD and penalty method for early exercise constraints.
result Pricing with ROMs is orders of magnitude faster than full order models.
Paper introduces CLVR to reduce price volatility in AMM exchanges.
problem Intra-block price volatility in AMM exchanges.
method CLVR constructs an ordering to minimize price volatility with low computation cost.
result CLVR minimizes price volatility with a small computation cost and can be externally verified.
This research creates efficient models for cyclo-stationary systems using generative methods.
problem Efficiently modeling systems with periodic forcing.
method Score-based generative modeling for reduced-order models.
result Accurately reproduces statistical properties and temporal correlations of cyclo-stationary time series.
The paper explores Lagrangians with simplified Euler-Lagrange equations.
problem Variational problems with Euler-Lagrange equations of reduced order.
method Geometrical construction to derive a family of Lagrangians.
result Lagrangians with reduced-order Euler-Lagrange equations are polynomials in the highest-order derivatives.
Odd primes act on alternating knots via flypes.
problem Understanding odd order group actions on alternating knots.
method Investigation of flypes between reduced alternating diagrams.
result Odd prime actions on alternating knots are isotopic through a single flype.
We show that wealth processes in the block-shaped order book model of Obizhaeva/Wang converge to their counterparts in the reduced-form model proposed by Almgren/Chriss, as the resilience of the order book tends to infinity. As an application of this limit theorem, we explain how to reduce portfolio choice in highly-re…
A new method predicts non-Markovian closure terms for complex systems.
problem Predicting the effect of unresolved variables on resolved dynamics in high-dimensional systems.
method Mamba-Assisted Closure (MAC) framework: sequence model trained to predict closure from resolved trajectory, coupled with reduced-order equations.
result Substantially outperforms existing methods in predictive accuracy and long-time stability.
Improved SVRG method using BB techniques for faster convergence.
problem Improving the convergence speed of stochastic variance reduction methods.
method Incorporates Barzilai-Borwein (BB) techniques as second-order information into SVRG.
result Proves linear convergence of the proposed method and its variants.
Paper presents ML approaches for faster brittle fracture modeling.
problem Faster modeling of brittle fracture in concrete.
method Machine learning algorithms combined with physics-based assumptions.
result ML models are orders of magnitude faster than high-fidelity models.
A generalized Lepage form for second-order Lagrangians is described.
problem Finding a Lepage equivalent for second-order Lagrangians.
method Using equivalence relation and preserving the order of Lagrangians.
result Completes attempts to find a Lepage equivalent for second-order Lagrangians.
Paper presents ZO-SVRG for faster nonconvex optimization.
problem Gradient-free optimization challenges in nonconvex settings.
method Comprehensive theoretical analysis, novel ZO-SVRG algorithm, accelerated versions.
result ZO-SVRG achieves best rate for ZO stochastic optimization.
New high-order scheme reduces BSDE truncation errors.
problem Numerical solution of backward stochastic differential equations (BSDEs).
method Proposes a new θ-scheme with careful θ selection for every subinterval. result Error estimates and verification of scheme order.
A model order reduction framework reduces financial risk analysis models efficiently.
problem Simulating high-dimensional financial risk models.
method Adaptive greedy sampling based on POD and surrogate modeling.
result Reduced models provide significant speedup with excellent accuracy.
New description of (1,1) L-space knots leads to non-left-orderable surgeries.
problem Characterizing and understanding (1,1) L-space knots. method Analyzing coherent reduced (1,1)-diagrams to describe (1,1) L-space knots and proving non-left-orderable fundamental groups. result Any L-space obtained by Dehn surgery on a (1,1)-knot in S3 has a non-left-orderable fundamental group. Optimal market making strategy with price forecasts reduces inventory costs and spreads.
problem Optimal market making strategy with price forecasts reduces inventory costs and spreads.
method Modeling market making strategy with linear price impact, random slope and intercept, and simultaneous order arrivals.
result Simultaneous order arrivals and price forecasts reduce inventory costs and spreads.
Study reduces financial dynamics complexity using PCA for NASDAQ, oil, gold, and USD.
problem Understanding complex financial interactions among multiple assets.
method Time-delay embedding and PCA for dimensionality reduction, followed by linear regression.
result Limited number of principal components capture dominant dynamics of each asset.
New method uses higher-order Langevin dynamics for efficient parallel sampling.
problem Efficient parallel sampling from high-dimensional log-concave distributions.
method Combines higher-order Langevin dynamics with blockwise Lagrange polynomial interpolation.
result Reduces the number of parallel points required for a target accuracy.
One popular approach to model the limit order books dynamics of the best bid and ask at level-1 is to use the reduced-form diffusion approximations. It is well known that the biggest contributing factor to the price movement is the imbalance of the best bid and ask. We investigate the data of the level-1 limit order bo…
Study of large group actions on surfaces, focusing on Hurwitz and handlebody groups.
problem Characterizing and understanding group actions on surfaces, especially maximal handlebody and Hurwitz groups.
method Analyzing various group actions, comparing Hurwitz and handlebody groups, and examining bounding actions.
result Relationship between Hurwitz groups and maximal handlebody groups, and insights into geometric bounding actions.
This work proposes a model for geodesic distances and flows on manifolds.
problem Geodesic distances and flows on differentiable manifolds.
method Manifold-augmented Eikonal equation solutions.
result Geodesic flow provides globally length-minimizing curves.
Improved robustness in optimization methods using second-order information.
problem Scalability and sensitivity to mini-batch size in optimization methods.
method Mini-Batch Stochastic Variance-Reduced Newton (extttMb−SVRN) algorithm incorporating partial second-order information. result Achieves a fast linear convergence rate independent of mini-batch size for large data sizes.
Generative network integrates into ROM for PDEs, matching measurements and estimating uncertainties.
problem Predicting and quantifying uncertainties in numerical simulations of PDEs.
method Generative network (GN) integrated into a reduced-order model (ROM) framework for inverse problems.
result GN-based ROM efficiently quantifies uncertainty and matches measurements with high accuracy.
Removes singularity order for Willmore immersions, reducing bubbling scenarios.
problem Understanding the singularity order of weak limits of Willmore immersions.
method Obtains removability result on singularity order, reducing bubbling scenarios.
result Only three out of twelve non-planar minimal surfaces may occur as bubbles of Willmore immersions.
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 paper proposes a new order slicing strategy to reduce market impact in large-volume trading.
problem Significant market impact and slippage in large-volume trading.
method Volatility-volume-based order slicing strategy using Exponential Weighted Moving Average and Markov Chain Monte Carlo simulations.
result Improves trade execution efficiency and reduces market impact.
A new model reduces the cost of simulating fluid flow through porous materials.
problem High computational cost of simulating fluid flow through porous materials.
method Proposes a fully probabilistic, Darcy-type reduced-order model.
result The model significantly accelerates uncertainty quantification tasks.
Paper develops a method for compact Markov modeling of time series data.
problem Compact representation of time-series data with reduced memory.
method Symbolic dynamics for partitioning, hierarchical clustering for state representation, Bayesian inference for parameter identification.
result Reduced-order Markov models capture system dynamics with minimal memory.
New method learns nonlinear projections for reduced-order modeling of complex dynamical systems.
problem Modeling transient dynamics near a manifold in nonlinear systems.
method Constrained autoencoder neural networks with invertible activation functions and biorthogonal weight matrices.
result Demonstrated effectiveness on a vortex shedding model, learning oblique fibers for fast dynamics.
Market impact is reduced when orders are filled with concentrated counterparts.
problem Market impact increases with a large number of trading counterparts.
method Analyzed London Stock Exchange data to show concentrated trading impacts market price.
result Concentrated trading reduces market impact when matched with similarly concentrated counterparts.
Study the stability of membranes using Helfrich energy and second variation formula.
problem Stability of membranes under various conditions.
method Developed and applied a second variation formula for the Helfrich energy for a class of surfaces.
result Studied the second variation of the area functional for a specific example.
New method calibrates stochastic reduced-order models from data efficiently.
problem Challenges in estimating drift and diffusion coefficients from data for high-dimensional systems.
method Uses a novel relationship between conditional score and transition density to constrain model coefficients directly from finite-lag statistics.
result Validated on various systems, the method reproduces statistical and dynamical properties of the original models.
This paper accelerates inverse solutions for PDEs using ML and ROMs.
problem Efficiently solving inverse problems governed by PDEs with many forward model solves.
method Combining ML with ROMs to improve accuracy and speed.
result ML-enhanced ROMs accelerate inverse problem solving.