New method simplifies checking consistency of differentiable loss functions.
problem Verifying consistency of differentiable loss functions is difficult.
method Developed a new approach called strong indirect elicitation (strong IE) to simplify checking consistency.
result Strong IE is equivalent to calibration for strongly convex, differentiable surrogates.
Differentiable pipeline replaces non-differentiable CAE components for shape optimization.
problem Gradient-based optimization is limited by non-differentiable components in CAE workflows.
method Surrogate models replace non-differentiable pipeline components, enabling gradient-based optimization.
result Gradient-based shape optimization possible without differentiable solvers.
Proposes a method for inference in high-dimensional classification with non-differentiable surrogate losses.
problem Lack of inference procedures for identifying driving factors in high-dimensional classification with non-differentiable surrogate losses.
method Kernel-smoothed decorrelated score and cross-fitted version for hypothesis tests and interval estimators.
result Valid and superior inference methods for high-dimensional classification with non-differentiable surrogate losses.
Optimize black-box simulators with local generative models.
problem Optimizing non-differentiable, stochastic simulators with intractable likelihoods.
method Differentiable local surrogate models based on deep generative models.
result Local surrogates enable gradient-based optimization, faster than baseline methods.
A new framework learns differentiable structured losses from data.
problem Learning effective losses for complex structured prediction tasks.
method Contrastive learning to learn differentiable structured losses from output data.
result Achieves similar or better performance than kernel-based methods.
Deep adaptive sampling improves surrogate modeling for complex systems.
problem Statistical errors in random sampling for high-dimensional problems.
method DAS^2 method, using deep generative models to refine training sets.
result Reduces statistical errors in approximating solutions for low-regularity problems.
Study proposes a differentiable surrogate loss function for optimizing Fβ score in binary classification with imbalanced data.
problem Non-differentiability of Fβ score makes it unsuitable for optimization by gradient-based learning. method Investigated relationship between Fβ score and loss functions, proposed a differentiable surrogate loss function. result Gradient paths of the proposed surrogate Fβ loss function approximate the gradient paths of the Fβ score. A new training method uses multilevel minimization for machine learning.
problem Training machine learning models with high variance and low efficiency.
method Constructs a multilevel hierarchy by reducing sample size and internally trains surrogate models with fewer samples.
result The multilevel method enhances model training efficiency compared to subsampled Newton's and variance reduction methods.
Gradient-informed BNNs improve Bayesian optimization performance.
problem Improving Bayesian optimization with gradient information.
method Gradient-informed loss function for Bayesian neural networks.
result Gradient information enhances BNN predictions and BO convergence.
This paper develops efficient surrogate models for optimization of complex dynamical systems.
problem Computational expense in solving complex dynamical systems through numerical simulation.
method Combination of proper orthogonal decomposition and radial basis functions for constructing low-dimensional surrogate models.
result Surrogate models reduce computational time for optimization problems while maintaining accuracy.
PANIS learns PDE surrogates for heterogeneous materials without solving the PDE.
problem Learning surrogates for parametrized PDEs in heterogeneous media.
method Physics-aware neural implicit solvers combining probabilistic learning and physics-informed discretization.
result Learned surrogates for effective solutions in heterogeneous materials without solving the reference problem.
Linear-Core Surrogates combine fast optimization and statistical efficiency in classification and structured prediction.
problem The trade-off between smoothness and margin-based losses in classification and structured prediction.
method Linear-Core (LC) Surrogates, a family of convex loss functions that stitch a linear core to a smooth tail.
result LC Surrogates achieve fast linear consistency rates while maintaining differentiability and strict H-consistency bounds. The minimization of loss functions is the heart and soul of Machine Learning. In this paper, we propose an off-the-shelf optimization approach that can minimize virtually any non-differentiable and non-decomposable loss function (e.g. Miss-classification Rate, AUC, F1, Jaccard Index, Mathew Correlation Coefficient, etc…
Paper discovers differential equations from data using neural networks and Bayesian methods.
problem Discovering differential equations from datasets using machine learning.
method Integrates neural network-based surrogates with Sparse Bayesian Learning (SBL).
result Proposes a robust model discovery algorithm and a Physics Informed Normalizing Flow (PINF).
A novel capsule network model improves surrogate modeling and uncertainty quantification from sparse data.
problem Surrogate modeling and uncertainty quantification of systems from sparse data.
method Adapted Capsule Network (CapsNet) architecture into image-to-image regression encoder-decoder network.
result The proposed approach accurately, efficiently, and robustly predicts responses for arbitrary diffusion fields.
Bayesian inverse problems solved with Gaussian models for PDEs.
problem Solving inverse problems with limited data for PDEs.
method Constructing PDE-informed Gaussian priors for Bayesian inversion.
result PDE-informed Gaussian priors outperform traditional priors.
Graph Neural Simulators improve data efficiency for PDE surrogates.
problem Lack of data efficiency in neural operators for PDE systems.
method Graph Neural Simulators (GNS) leverage message-passing and numerical time-stepping to learn PDE dynamics efficiently.
result GNS achieves less than 1% relative L2 error using only 3% of available trajectories.
Bayes-consistent disagreement discrepancy loss improves model robustness.
problem Distribution shift in real-world neural network deployment.
method Introducing a novel disagreement loss that is Bayes consistent.
result Proves existing surrogates for disagreement discrepancy are not Bayes consistent.
We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for determining how accurate the model predictions are and identifying which input …
SURGIN uses generative models to infer subsurface flow data efficiently.
problem Inefficient and task-specific inversion methods for subsurface multiphase flow.
method SURGIN integrates U-FNO surrogate with SGM for zero-shot conditional generation.
result Decent inference of heterogeneous geological fields and flow dynamics with uncertainty quantification.
New method speeds up Bayesian inverse problem solving with neural operators.
problem Solving infinite-dimensional Bayesian inverse problems with high computational cost.
method Delayed-acceptance geometric MCMC driven by derivative-informed neural operator surrogates.
result Significant speedup in generating posterior samples (3-9 times faster).
Derivative-informed models improve financial surrogates for accurate hedging and risk management.
problem Developing fast surrogate models for financial derivatives and risk quantities.
method Derivative-informed operator learning framework combining neural operators, random features, and tangent sensitivity equations.
result The framework reduces hedging and risk errors by 40-76% compared to standard surrogates.
DeepONets improve surrogate modeling for engineering systems.
problem Accurately modeling complex PDEs for engineering systems.
method DeepONets specialize in approximating mathematical operators for PDEs.
result DeepONets achieve high prediction accuracy and zero-shot capability.
Proposes a method to improve surrogate models by incorporating sensitivity information.
problem Pruned neural networks often fail to capture sensitivities and uncertainties of original models.
method Combines Interval Adjoint Significance Analysis and Sobolev Training to accurately model sensitivities.
result Pruned models based on the proposed method better match original sensitivities.
Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.
Bayesian Gaussian process models handle uncertain data locations in PDE approximations.
problem Handling uncertainties in data locations for PDE approximations.
method Bayesian inference of uncertain inputs integrated into Gaussian process predictions.
result Substantial reduction in predictive uncertainties achieved through Bayesian inference.
This study proposes an efficient surrogate for Darcy flow inverse problems.
problem Efficiently constructing accurate surrogate models for high-dimensional complex inverse problems.
method Sequential Bayesian design strategy to acquire a locally accurate surrogate model focusing on high-probability regions.
result The proposed method accelerates inversion accuracy and computational speed.
Study on H-consistency bounds for machine learning surrogates.
problem Estimating target loss error relative to surrogate loss error in machine learning.
method Developed H-consistency bounds for various surrogates and loss functions. result Stronger guarantees than existing methods, offering distribution-dependent and -independent bounds.
SCaSML improves PDE solvers by correcting errors efficiently.
problem Reliable and error-free high-dimensional PDE solutions.
method Defect correction method to derive a Structural-preserving Law of Defect.
result SCaSML achieves faster convergence and reduced errors in high-dimensional PDEs.
Several tasks in machine learning are evaluated using non-differentiable metrics such as mean average precision or Spearman correlation. However, their non-differentiability prevents from using them as objective functions in a learning framework. Surrogate and relaxation methods exist but tend to be specific to a given…
New method reduces PDE surrogate model training costs by selectively acquiring time steps.
problem High computational cost of generating training data for PDE surrogate models.
method STAP (Selective Time-Step Acquisition for PDEs) framework that acquires only important time steps.
result Demonstrated effectiveness on several benchmark PDEs, reducing training costs.
We propose a new framework to improve the calibration of neural networks.
problem Improving the accuracy of model confidence predictions.
method Introducing a differentiable surrogate for expected calibration error (DECE) and a meta-learning framework to optimise model hyper-parameters for validation set calibration.
result Achieved competitive performance with existing calibration approaches.
BITS for GAPS uses Bayesian methods to improve surrogate model accuracy in complex systems.
problem Improving surrogate model accuracy in complex physical systems with uncertainty.
method Bayesian Information-Theoretic Sampling for hierarchical Gaussian Process Surrogates.
result Increased expected information gain and predictive accuracy by targeting high-uncertainty regions.
Proposes a method to train neural networks that solve differential equations faster.
problem Training neural networks that solve differential equations becomes computationally expensive.
method Introduces a differentiable surrogate for numerical solver time cost using higher-order derivatives.
result Trains models that are faster to solve while maintaining nearly the same accuracy.
A new differentiable resampling method for Monte Carlo simulations.
problem Improving the efficiency and differentiability of resampling in Monte Carlo simulations.
method Proposes a diffusion model surrogate for resampling, proving consistency and outperforming existing methods.
result The proposed method outperforms state-of-the-art differentiable resampling methods on various benchmarks.
A new framework reduces inconsistencies in chaotic surrogate modeling.
problem Consistency issues between probabilistic objectives and dynamical system dynamics.
method KAFFEE (Kalman-Aware Framework For Ergodic Emulation), a differentiable extended Kalman filter.
result KAFFEE mitigates the dynamic-probabilistic consistency gap, improving reconstruction and predictive scores.
TREX explains tree ensembles by identifying key training examples.
problem Identifying which training examples most influence tree ensemble predictions.
method TREX builds a surrogate model using a kernel that captures tree ensemble structure, approximating the original model.
result TREX provides accurate and effective explanations for tree ensembles.
Develops a neural surrogate for proton dose calculation using Monte Carlo dropout uncertainty.
problem Computational demand in proton therapy workflows requiring repeated evaluations.
method Integrates Monte Carlo dropout into a neural network surrogate for fast, differentiable dose predictions and uncertainty quantification.
result Shows significant speedups over MC while retaining uncertainty information.
We develop DTs for PDE models using KL-NN and TL, analyzing TL's moment equations and one-shot learning for exactness.
problem Creating accurate digital twins for systems governed by PDEs under changing conditions.
method We use KL-NN surrogate models and transfer learning to construct DTs, analyzing the moment equations and proposing one-shot and few-shot learning methods.
result For linear PDEs, one-shot TL is exact; for nonlinear PDEs, some parameters can be transferred with minimal error.
PILNO uses neural operators to solve PDEs efficiently on point clouds.
problem Solving partial differential equations (PDEs) on point cloud data efficiently.
method Physics-informed low-rank neural operator framework combining low-rank kernel approximations and an encoder-decoder architecture.
result PILNO efficiently approximates solution operators of PDEs on point cloud data, satisfying PDE constraints and boundary conditions.
A new method combines SciML and UQ with physical constraints.
problem Uncertainty quantification in scientific machine learning tasks.
method Physics-constrained polynomial chaos expansion.
result Effective uncertainty quantification and SciML integration.
DPC uses physics and neural nets to solve SDEs.
problem Solving stochastic differential equations with missing physics.
method Physics-data fusion with conditional maximum mean discrepancy (CMMD) loss.
result DPC achieves highly accurate solutions on benchmark examples.
New insights into quantized neural networks reveal learning dynamics and generalization errors.
problem Understanding the impact of quantization hyperparameters on learning dynamics in high-dimensional models.
method Theoretical analysis and fixed-point analysis of STE dynamics in quantized models.
result STE training in quantized models converges to a plateau followed by a sharp drop in generalization error, influenced by quantization range.
We learn a compact surrogate model for optimization problems to reduce training and inference time.
problem Solving optimization problems with unknown parameters is computationally expensive and may lead to suboptimal solutions.
method We represent the optimization problem in terms of meta-variables and learn a low-dimensional surrogate model end-to-end with the predictive model.
result We achieve a large reduction in training and inference time, and improved performance.
Real-world applications often involve domain-specific and task-based performance objectives that are not captured by the standard machine learning losses, but are critical for decision making. A key challenge for direct integration of more meaningful domain and task-based evaluation criteria into an end-to-end gradient…
Efficient surrogate modeling for complex PDEs with physical laws.
problem High computational cost of repeated PDE simulations.
method LC-prior Gaussian process with POD and RBF-FD.
result Significantly reduced computational cost and improved accuracy.
Researchers develop methods to recover agent behavior from sparse data using Gaussian processes.
problem Recovering agent behavior from limited, noisy data in potential mean field games.
method Two Gaussian process-based frameworks: inf-sup formulation and bilevel approach.
result Surrogate MFG models can accurately reproduce observed data, even when prior information is limited.
Optimizes maps with controlled distortion for geometric tasks.
problem Free-boundary diffeomorphism optimization in geometric modeling.
method Least-squares quasiconformal (LSQC) operator and Spectral Beltrami Network (SBN).
result LSQC minimizer well-posed under mild conditions, stable under mesh refinement.