In many digital twin (DT) applications, the complexity of the forward models, the high dimensionality of the inference parameter and decision variable spaces, the need for real-time response, and the imperative of accounting for uncertainties all conspire to make the underlying inverse and optimal control problems intractable using high fidelity forward models. Surrogates and reduced order models (ROMs) can make these tasks tractable, provided they are sufficiently accurate and can be constructed with sufficiently few forward model solves.
Specific challenges arising in the DT setting and that will be addressed in this workshop include: (1) The surrogates/ROMs need not represent the full spatiotemporal system dynamics well, but only the control objectives and data assimilation observables—how this “goal-orientation” is best done remains a challenge; (2) since DTs typically evolve the dynamics over long time periods, there is a need to make ROMs structure preserving (e.g., energy conserving); (3) Neural network representations have shown much promise as surrogates in high dimensions, but work remains to be done to provide guarantees of their trustworthiness, particularly in the few data regime; (4) the surrogates/ROMs must be parametric with respect to not just state space, but also control variable space and uncertain parameter space, since the DT framework executes data assimilation and control problems repeatedly over a moving horizon; (5) many methods for surrogates rely on an intrinsically low-dimensional map from parameters to outputs of interest, and for ROMs an intrinsically low-dimensional solution manifold, yet linear subspaces may not capture this low-dimensionality efficiently for certain classes of problems (e.g., high frequency wave propagation, advection-dominated flow and transport); and (6) using surrogates trained on samples of high-fidelity input–output maps and not their Jacobians can result in poor approximation of gradients, leading to inaccurate solutions of optimization problems underlying data assimilation and optimal control.
Funding
All funding has been allocated for this event.
Poster Session
This workshop will include a poster session for early career researchers (including graduate students). In order to propose a poster, you must first register for the workshop, and then submit a proposal using the form that will become available on this page after you register. The registration form should not be used to propose a poster.
The deadline for proposing is September 14, 2025. If your proposal is accepted, you should plan to attend the event in-person.
Gianluigi Rozza
SISSA – International School for Advanced Studies
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Robert Scheichl
Universität Heidelberg
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Paul Schwerdtner
Courant Institute of Mathematical Sciences at New York University
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Daniel Tartakovsky
Stanford University
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Steffen Werner
Virginia Tech
Schedule
Monday, November 10, 2025
8:30-8:55 CST
Breakfast/Check-in
8:55-9:00 CST
Welcome
9:00-9:40 CST
Amortized Full-Waveform Inference with learned Summary Statistics
Speaker: Felix Herrmann (Georgia Institute of Technology)
During this talk, I will discuss different Bayesian inference techniques we have developed in my group. The problem of Full-Waveform Inference is challenged by the large degrees of freedom, the expensive to evaluate forward operators, and the presence of parasitic local minima. In an effort to meet these challenges, we combine techniques from amortized simulation-based inference, generative models, and a hybrid of physics-based learned summary statistics. Our approach not only reduces dimensionality of the seismic data but it also simplifies the model-to-summarized data mapping while preserving information, so the posterior distribution remains informed.
9:40-9:50 CST
Q&A
9:50-10:20 CST
Coffee Break
10:20-11:00 CST
Complexity reduction in the solution of parametrized PDEs
Speaker: Stefania Fresca (University of Washington)
11:00-11:10 CST
Q&A
11:10-11:35 CST
Coffee Break
11:35-12:15 CST
Quadratic approximations for model order reduction and sparse regression
Speaker: Paul Schwerdtner (New York University)
We develop scalable quadratic manifolds (QMs) that enrich linear subspaces with quadratic corrections for accurate nonlinear dimensionality reduction. A greedy basis-construction strategy that selects basis vectors from both leading and later principal components targets directions that are most profitably corrected by quadratic terms. Coupled with linear-algebra reformulations and streaming computation, the method builds QMs from massive, high-dimensional snapshot data while maintaining smooth, well-conditioned embeddings suited for downstream modeling.
We then present two extensions. First, quadratic-manifold sparse regression combines the greedy training with nonlinear projection operators to reconstruct fields from sparse samples far more accurately than linear approaches. Second, operator-inference-aware training augments the objective with the reduced-model prediction error, which suppresses oscillatory embeddings and yields much stabler surrogate dynamics. Together, these advances provide a practical toolkit for large-scale model reduction and sparse reconstruction in transport- and turbulence-dominated settings.
12:15-12:25 CST
Q&A
12:25-13:35 CST
Lunch Break
13:35-14:15 CST
Reduced-order models informed by observations and simulated data
Speaker: Daniel Tartakovsky (Stanford University)
14:15-14:25 CST
Q&A
14:25-14:40 CST
Coffee Break
14:40-14:55 CST
Short Talk: Provable in-context learning of PDEs
Speaker: Yulong Lu (University of Minnesota, Twin Cities)
Transformer-based foundation models, pre-trained on a wide range of tasks with large datasets, demonstrate remarkable adaptability to diverse downstream applications, even with limited data. One of the most striking features of these models is their in-context learning (ICL) capability: when presented with a prompt containing examples from a new task alongside a query, they can make accurate predictions without requiring parameter updates. This emergent behavior has been recognized as a paradigm shift in transformers, though its theoretical underpinnings remain underexplored. In this talk, I will discuss some recent theoretical understandings of ICL for PDEs, emphasizing its approximation power and generalization capabilities. The theoretical analysis will focus on two scientific problems: elliptic PDEs and stochastic dynamical systems.
14:55-15:05 CST
Q&A
15:05-15:30 CST
Lightning Talks
15:30-16:30 CST
Social Hour and Poster Session
Tuesday, November 11, 2025
8:30-9:00 CST
Breakfast/Check-in
9:00-9:40 CST
Learning dynamical systems from time- and frequency-response data
Speaker: Serkan Gugercin (Virginia Polytechnic Institute & State University (Virginia Tech))
Dynamical systems are a principal tool in the modeling, prediction, and control of physical phenomena with applications ranging from structural health monitoring to electrical power network dynamics. Direct numerical simulation of these mathematical models may be the only possibility for accurate prediction or control of such complex phenomena. However, in many instances, a high-fidelity mathematical model describing the dynamics is not readily available. Instead, one has access to an abundant amount of input/output data via either experimental measurements or a black-box simulation. The goal of data-driven modeling is, then, to accurately model the underlying dynamics using input/output data only. In this talk, we will investigate various approaches to data driven modeling of dynamical systems using systems-theoretical concepts. We will consider both frequency-domain and time-domain measurements of a dynamical system including parametrically varying dynamics. In some instances, we will have true experimental data, and in others we will have access to simulation data. We will illustrate these concepts in various examples.
9:40-9:50 CST
Q&A
9:50-10:20 CST
Coffee Break
10:20-11:00 CST
Data Assimilation of Hamiltonian Flows
Speaker: Olga Mula (University of Chicago)
Hamiltonian flows are challenging for data assimilation because solutions have often low regularity, they are spatially localized, and the evolution preserves certain quantities which one would like to discover and then preserve in the reconstruction. In this talk, I will present a data assimilation algorithm formulated in continuous time, and which can be implemented after time discretization.
Two main ingredients of the algorithm are symplectic dynamical approximations, and a dynamic strategy to position sensors.
11:00-11:10 CST
Q&A
11:10-11:35 CST
Coffee Break
11:35-11:55 CST
Short talk: Reduced-order modeling for digital twins in the process industry: application to carbon dioxide methanation reactors
Speaker: Ion Victor Gosea (Brigham Young University)
A digital twin is a virtual representation of a physical process, continuously updated with real-time data from its physical counterpart. This link between the two entities (physical and digital) needs to be dynamic, allowing for the simulation, analysis, and monitoring of the physical asset, enabling optimized decision-making for maintenance and operational improvements. Classical model-based approaches are typically demanding in terms of running time and memory and can hardly accommodate real-time changes in operating conditions. This limits, to some extent, their application in complex real-time scenarios.
Reduced-order modeling (ROM) is an essential step that enables digital twinning by incorporating measured data into the loop and ensuring that the surrogate is swiftly computed and updated. In this study, we examine several techniques for ROM of dynamical processes, including extensions of the classical methods known as operator inference (OpInf) and sparse identification (SINDy). These methods are evaluated for their ability to model and control the dynamic operation of the case study, e.g., a catalytic Power-to-X reactor; this is a key technology for converting renewable electricity into synthetic fuels or platform chemicals. Power-to-X systems are essential for long-term energy storage and mitigating the mismatch between intermittent renewable generation and demand.
We show how snapshot data collected during process operation can be used to extract valuable information. This is used for controlling and predicting the complex processes that faithfully describe the physics of the catalytic carbon dioxide methanation reactor under a variety of parameters and conditions. By evaluating the accuracy and computational efficiency of these methods, we aim to identify suitable reduced-order predictive surrogate models tailored to the challenging application under study. If time permits, discussions on robustness to noisy or hidden/incomplete data will be added, and also on including a nonlinear convolutional neural network (CNN) decoder to enrich the reconstruction capabilities.
11:55-12:15 CST
Short Talk: Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces
Speaker: Shane McQuarrie (Max Planck Institute for Dynamics of Complex Technical Systems)
We present an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. The approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.
12:15-12:25 CST
Q&A
12:25-13:40 CST
Lunch Break
13:40-14:20 CST
Localized Model Order Reduction via Multiscale Spectral Generalised Finite Elements
Speaker: Robert Scheichl (Heidelberg University)
Multiscale Spectral Generalized Finite Element Methods (MS-GFEM) are a powerful new discretisation method for general variational problems that satisfy a Gårding-type inequality, including strongly non-Hermitian problems. The construction of optimal approximation spaces is localised and requires no a priori regularity assumptions. The global approximation error is controlled by the local errors, which are rigorously shown to decay nearly exponentially. The optimality hinges on an SVD of the local restriction operator in a suitable, coefficient-dependent inner product on an oversampled patch. Compactness of this operator in the space of a-harmonic functions guarantees spectral accuracy akin to Weyl asymptotics for the Laplacian. As such, MS-GFEM can be seen as an “hp-version” of Localized Orthogonal Decomposition (LOD). Given the coefficient function the local approximation spaces can be constructed efficiently. In this talk, I will show how we can use Grassmannian interpolation of the resulting local approximation spaces on sparse grids in high dimensions to derive localized model order reduction methods that inherit the nearly exponential spatial convergence of MS-GFEM and parametric convergence of sparse grids. I will show some numerical experiments confirming the theoretical results in the context of elliptic problems.
14:20-14:30 CST
Q&A
14:30-15:00 CST
Coffee Break
15:00-15:40 CST
Data-driven Balanced Truncation for Learning Mechanical Systems
Speaker: Steffen Werner (Virginia Polytechnic Institute & State University (Virginia Tech))
Learning dynamical systems from data has emerged as a pivotal area of research, bridging the realms of mathematics, engineering, and data science. Dynamical systems, which describe how states evolve over time based on underlying mathematical relations, are fundamental for understanding a wide range of time-dependent phenomena. For the use of these systems in practical applications including the design of digital twins, high modeling accuracy as well as interpretability and explainability are essential. All of these desired properties are strongly tied to the internal mathematical structure of the dynamical systems. For example, in the modeling of mechanical or electro-mechanical processes, typically systems with second-order time derivatives occur. In this case, data are usually given in the frequency domain as samples of the corresponding transfer function. To learn such structured systems from frequency domain data, we develop in this work a data-driven second-order balanced truncation approach. This method allows the construction of low-dimensional second-order systems with generalized proportional damping structure by assembling appropriate Loewner-like matrices. Numerical examples demonstrate the effectiveness of the proposed method.
15:40-15:50 CST
Q&A
Wednesday, November 12, 2025
8:30-9:00 CST
Breakfast/Check-in
9:00-9:40 CST
Stable nonlinear manifold approximation with composition networks
Speaker: Anthony Nouy (Centrale Nantes, Nantes Université)
We consider the problem of approximating a subset $M$ of a Banach space $X$ by a low-dimensional manifold $M_n$. A large class of nonlinear methods can be described by a decoder $D: mathbb{R}^n to X$ whose range is the nonlinear manifold $M_n$, and an encoder $E : M to mathbb{R}^n$ which extracts $n$ pieces of information $E(u)$ from an element $u$ in $M$. Here, we introduce a nonlinear method where $E$ is linear and $D$ is a stable decoder which is obtained by a tree-structured composition of polynomial maps, estimated sequentially from samples in $M$. Rigorous error and stability analyses are provided, as well as an adaptive strategy for constructing a decoder which guarantees an approximation of the set $M$ with controlled mean-squared or wort-case errors, and a controlled stability (Lipschitz continuity) of the encoder and decoder pair. Also, we discuss on the definition of optimal encoders and provide concrete strategies for their estimation.
This is joint work with Antoine Bensallah and Joel Soffo.
Reference:
A. Bensalah, A. Nouy, and J. Soffo (2025). Nonlinear manifold approximation using compositional polynomial networks. arXiv e-prints arXiv:2502.05088, Feb. 2025.
9:40-9:50 CST
Q&A
9:50-10:20 CST
Coffee Break
10:20-11:00 CST
Dynamical model order reduction of parametric particle-based kinetic plasma models
Speaker: Cecilia Pagliantini (University of Pisa)
In this talk we discuss an adaptive model order reduction and hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation.
11:00-11:10 CST
Q&A
11:10-11:35 CST
Coffee Break
11:35-12:15 CST
Optimization for Low Dimensional Modeling
Speaker: Laura Balzano (University of Michigan)
12:15-12:25 CST
Q&A
12:25-13:40 CST
Lunch break
13:40-14:20 CST
Enhancing CFD simulations for digital twins by model reduction and scientific machine learning
Speaker: Gianluigi Rozza (SISSA)
Partial differential equations (PDEs) are invaluable tools for modelling complex physical phenomena. However, only a limited number of PDEs can be solved analytically, leaving the majority of them requiring computationally expensive numerical approximations. To address this challenge, reduced order models (ROMs) have emerged as a promising field in computational sciences, offering efficient computational tools for real-time simulations. In recent years, deep learning techniques have played a pivotal role in advancing efficient ROM methods with exceptional generalisation capabilities and reduced computational costs to enhance surrogate simulation tools.In this talk we explore how classical ROM techniques can be elevated through the integration of some deep learning models in view of more demanding applications involving digital twins. We will introduce hybrid approaches, which consider both physics-based and purely data-driven techniques, as well as aggregated ones, where the model is built as the combination of different pre-trained models.Our discussion encompasses a review of existing (intrusive and data driven) approaches to enhancing ROM by means of neural operators with applications in Computational Fluid Dynamics, also in presence of turbulence and compressibility.
14:20-14:30 CST
Q&A
14:30-15:00 CST
Coffee Break
15:00-16:00 CST
Roundtable Discussion: Challenges and Opportunities in Reduced Order and Surrogate Modeling for Digital Twins
Thursday, November 13, 2025
8:30-9:00 CST
Breakfast/Check-in
9:00-9:40 CST
Scalable Reduced Order Modelling For Digital Twins – Hype or Reality
Speaker: Dirk Hartmann (Siemens - Digital Industry Software)
The concept of Digital Twins has emerged more than a decade ago and has been promoted still then as a potential solution for many industrial challenges. Still their industrial adoption is limited to high value use cases only. Scalable solutions and workflows to build real-time models as required for most Digital Twin applications are missing. Reduced Order Modelling approaches offer unique approaches to do so.
In this talk, we review the-state-of-the art industrial Surrogate Modelling approaches focusing on POD-based methods as well as brute force Machine Learning based Surrogate Modelling approaches. We highlight the most important application domains as well as concrete use cases. We conclude with a summary of major obstacles limiting broader industrial adoption today with the goal to spur further research to address the problem as well as to initiate new research collaborations.
9:40-9:50 CST
Q&A
9:50-10:20 CST
Coffee Break
10:20-11:00 CST
Real Time High Fidelity Bayesian Inversion, Prediction, and
Optimal Sensor Placement for Large Scale LTI Systems Governed by
Wave Equations, with Application to a Digital Twin for Tsunami Early
Warning
Speaker: Omar Ghattas (University of Texas at Austin)
We address Bayesian inverse problems governed by autonomous dynamical
systems, and in particular linear time-invariant (LTI) systems. Our
focus is on large-scale source inversion problems in which real-time
solution and uncertainty quantification are critical, and hyperbolic
or nearly-hyperbolic forward PDEs govern the dynamics (e.g., high
frequency acoustic, elastic, or electromagnetic wave propagation or
advection-dominated transport). Such PDEs do not readily lend
themselves to classical surrogate or reduced order representations due
to large Kolmogorov n-widths. We show that the parameter-to-observable
(p2o) operator inherits the autonomous structure of the forward
problem, in particular the time shift invariance. Upon discretization,
this leads to a block Toeplitz matrix, permitting compact storage, FFT
diagonalization, and fast GPU implementation. Thus evaluation of the
p2o map using this representation can be carried out exactly (up to
rounding errors) many orders of magnitude faster than the PDE-based
p2o map. The fast p2o map computation can be exploited to compute the
Bayesian solution of the source inversion problem in real time. We
present results for a tsunami early warning inverse and posterior
prediction problem with one billion inversion parameters representing
the earthquake-induced seafloor motion. The observational data come
from acoustic pressure sensor data. The inverse solution and
subsequent tsunami wave height forecasts can be computed online in a
fraction of a second on a 512-GPU cluster (compared to ~50 years using
the full wave propagation PDEs on the same cluster). Moreover, we
exploit this capability for fast Bayesian inversion to determine the
sensor placement that maximizes the expected information gain from the
data using a greedy algorithm.
This work is joint with Sreeram Venkat (UT Austin), Stefan Henneking
(UT Austin), and Alice Gabriel (UCSD).
11:00-11:10 CST
Q&A
11:10-11:35 CST
Coffee Break
11:35-11:55 CST
Short Talk: Reduced basis methods for radiative transfer equation
Speaker: Fengyan Li (Rensselaer Polytechnic Institute)
Radiative transfer equations (RTEs) are fundamental models to describe the physical phenomena of energy or particle transport through mediums that are affected by absorption, emission, and scattering processes. Deterministic simulations can provide an accurate description of the solutions; they however face many computational challenges, most prominently the need to compute the angular flux defined in the high dimensional phase space. In this talk, we will share our work in developing reduced basis methods (RBMs) for the stationary RTE. In the single-query setting, our RBM is designed by leveraging the low-rank structure of the angle-induced solution manifold in or near the scattering dominant regime. In the multi-query setting, four RBM-based ROMs are formulated for the parametric RTE, with one major technical focus on implementation strategies, to ensure ultimate efficiency and robustness of the entire model reduction algorithm under the affine assumption of the parameter dependence. The work is in collaboration with Y. Chen (UMass Dartmouth), Y. Cheng (Virginia Tech), Kimberly Matsuda (Rensselaer Polytechnic Institute) and Z. Peng (Hong Kong Univ. of Science and Technology).
11:55-12:15 CST
Short talk: A geometric view of adaptive surrogate modeling for predictive control over state, control and parameter spaces
Speaker: Hassan Iqbal (University of Texas, Austin)
Model predictive control can be considered a form of suboptimal control technique that works well if the system model is known and sufficient compute is available for online computations. In practice, we may not have exact knowledge of the system dynamics, and the computation may be too costly. To accelerate solution to these systems, we propose a learning-based framework that combines 1) function encoder to approximate the system dynamics for parametric families of differential equations in a geometrically interpretable way, and to rapidly identify dynamics online from a single trajectory in a zero-shot (retraining free) manner, and 2) differentiable predictive control for offline pretraining of parametric control policies. Efficacy of the proposed method is verified across a range of nonlinear systems with varying dimensionality. Time permitting, I will briefly motivate a physics-guided conditioning method for message-passing graph neural networks to achieve material-adaptive granular flows in low-data regimes.
12:15-12:25 CST
Q&A
12:25-13:40 CST
Lunch break
13:40-14:20 CST
Advances in certifiable model reduction: parametric LTI systems and operator learning
Speaker: Akil Narayan (University of Utah)
For outer loop applications such as uncertainty quantification, control, and optimization, building certifiably accurate surrogate and reduced order models (ROM) is of particular importance, especially these outer loop goals are part of a digital twin infrastructure. We present recent work on two new approaches for surrogate model/ROM constructions that come with new and useful attractive versions of certifiability. The first approach is a ROM construction for parametric linear dynamical systems that provides both an a priori and a posteriori understanding of ROM error. The second approach addresses supervised operator learning that provides sample complexity estimates for stability and accuracy. Of particular interest is the ability of this approach to provide error in high-regularity norms, e.g., Sobolev norms. We will discuss promises and pitfalls of these approaches, and present an outlook toward adaptive constructions, uncertainty estimates, and nonlinear model reduction and surrogate construction.
14:20-14:30 CST
Q&A
14:35-15:00 CST
Coffee Break
15:00-15:40 CST
Nested Operator Inference for data-driven learning of physics-based reduced-order models
Speaker: Nicole Aretz (University of Texas of Austin)
Highly accurate full-order models are often too expensive computationally to evaluate in predictive, real-time, or many-query applications. Projection-based model order reduction methods exploit the intrinsic low-dimensionality of the full-order solution manifold. These reduced-order models (ROMs) typically achieve significant computational savings while remaining physically interpretable through the governing equations. Operator Inference (OpInf) is a data-driven learning technique to construct projection-based ROMs without accessing the full-order operators. Because the degrees of freedom in the classic OpInf learning problem scale polynomially in the dimension of the reduced space, classic OpInf requires precise regularization to balance the numerical stability of the OpInf learning problem, the structural stability of the learned ROM, and the achieved reconstruction accuracy. Nested OpInf exploits the inherent hierarchy within the reduced space to iteratively construct initial guesses for the OpInf learning problem that prioritize the interactions of the dominant modes. The initial guess computed for any target reduced dimension corresponds to a ROM with provably smaller or equal snapshot reconstruction error than with standard OpInf. We demonstrate the nested OpInf algorithm on a cubic heat conduction problem and a large-scale, parameterized model of the Greenland ice sheet.
15:40-15:50 CST
Q&A
Friday, November 14, 2025
8:30-9:00 CST
Breakfast/Check-in
9:00-9:40 CST
Multimodal data and model fusion for the atmosphere using diffusion models
Speaker: Romit Maulik (Pennsylvania State University)
9:40-9:50 CST
Q&A
9:50-10:20 CST
Coffee Break
10:20-11:00 CST
TBA
Speaker: Carmen Grässle (Technische Universität Braunschweig)
11:00-11:10 CST
Q&A
11:10-11:35 CST
Coffee Break
11:35-12:15 CST
A randomized Greedy algorithm with certification over the entire parameter set.
Speaker: Charles Beall (Stevens Institute of Technology)
We design a randomized Greedy algorithm that draws parameter samples from a clever probability distribution to effectively build a training set at each iteration. We prove that this algorithm provides certification with high probability over the entire parameter set, utilizing results from sampling discretization theory and concentration of measure phenomena. Moreover, we demonstrate favorable properties of the algorithm’s sampling complexity to break the curse of dimensionality encountered by e.g. the deterministic Greedy algorithm when choosing a suitable training set. We present preliminary numerical results of the algorithm’s performance at building reduced approximation spaces for benchmark PDE problems. Finally, we discuss potential applications of the algorithm in the setting of localized model order reduction for linear and nonlinear PDEs. Within the digital twin framework, this approach would potentially allow for an efficient construction of reduced local approximation spaces that accurately capture multiscale aspects of the system with high probability, even for parameters not seen in the training phase.
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