Related papers: CONFIDE: Contextual Finite Differences Modelling o…
The paper considers the problem of multi-objective decision support when outcomes are uncertain. We extend the concept of Pareto-efficient decisions to take into account the uncertainty of decision outcomes across varying contexts. This…
Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using…
Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…
We propose a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations. We formulate the problem of inferring constitutive relations from experiments as an indirect inverse…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
Deep neural networks are behind many of the recent successes in machine learning applications. However, these models can produce overconfident decisions while encountering out-of-distribution (OOD) examples or making a wrong prediction.…
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…
State-of-the-art models often make use of superficial patterns in the data that do not generalize well to out-of-domain or adversarial settings. For example, textual entailment models often learn that particular key words imply entailment,…
This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute…
Structured prediction models aim at solving a type of problem where the output is a complex structure, rather than a single variable. Performing knowledge distillation for such models is not trivial due to their exponentially large output…
Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…
Causal inference is essential for data-driven decision making across domains such as business engagement, medical treatment and policy making. However, research on causal discovery has evolved separately from inference methods, preventing…
Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters,…
We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
We explore a new simulation scheme for partial differential equations (PDE's) called Information Field Dynamics (IFD). Information field dynamics attempts to improve on existing simulation schemes by incorporating Bayesian field inference,…
SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton et al., 2016]. In this article, we propose an extension of the SINDy method that learns systems of…
Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent…
A novel refinement measure for non-intrusive surrogate modelling of partial differential equations (PDEs) with uncertain parameters is proposed. Our approach uses an empirical interpolation procedure, where the proposed refinement measure…