What is the difference between deterministic and stochastic models?

Ever wonder how weather forecasts or traffic predictions are made? That's where deterministic models come in! These models are like roadmaps for scientists and analysts, helping them predict outcomes based on set rules and known variables. Imagine playing a board game with fixed rules—each move you make follows a predictable path. Similarly, deterministic models use known data to forecast future events, providing a clear picture of what might happen. While they're precise and useful in many fields like finance and engineering, they work best when everything follows a set pattern, much like a well-structured game plan.

In the geosciences world a determisistic model will only use one value for one parameter used in the modeling. Given that the inverse problem is vastly under constrained and that values of parameters are in fact unknown (though likely to be within a certain range) a deterministic reservoir model is ALWAYS wrong and the forecast will ALWAYS be off. However it can usually be made quite simply

Deterministic models are 'near-to-exact' models. They are modelled out of physical, chemical, thermodynamic laws ,and to a certain degree of precision, are of causal premise. A deterministic models produces the same exact results for a particular set of inputs. It is repeatable, because for known input (at least seen once!) we can determine precisely the output up to a certain degree of tolerated error due to either disturbance or perturbation. Examples of deterministic models are any system which can be modelled with differential equations, algebraic state-space determination and classification models.

A deterministic system assumes an exact relationship between variables. As a result of this relationship between variables, it enables one to predict and notice how variables affect the other. For example, If one assumes that X (Ram) is 4 times taller than Y (Rohan), then the equation will be X = 4Y.

In the geosciences world, rather than "a" stochastic model (which is somewhat of an oxymore) one should talk about stochastic modeling, or preferably uncertainty modeling, and the range of models associated with a set of probability functions attached to the input parameters. Any one realization of the model will be wrong; however if the input parameter distribution is correctly apprehended the envelope of results (such as hydrocarbon in place, production profiles, reserves ...) should bracket the actual outcomes

Here are some examples of stochastic models: Markov chains A stochastic model that uses mathematics to predict the probability of a sequence of events based on the most recent event. Markov A stochastic model that describes a sequence directed graph that can be used to measure shopping page performance. In this model, the touchpoint is the vertex, and the edges define the transition probability from the source node to the destination node. Poisson process A stochastic process that models a series of discrete events that occur at random when the average of the events is known. GARCH model A stochastic process with many applications, including empirical finance.

Ever wondered how randomness affects predictions in gambling or stock markets? Enter stochastic models! Unlike deterministic models, stochastic ones embrace uncertainty. They're like a dice roll, where outcomes aren't fixed but based on probabilities. Picture predicting tomorrow's weather by considering various possibilities, not just one path. These models capture randomness, offering insights into complex systems like financial markets or biological processes. While they can't predict specific outcomes, they help understand and estimate probabilities, making them vital in fields where uncertainty plays a big role.

Stochastic models are systems which are not deterministic, nor predictive, in that they have randomness induced in their behaviour. Stochastic models present data and predicts outcomes that account for certain levels of unpredictability or randomness. Examples of stochastic models are Monte Carlo Simulation, Regression Models, and Markov-Chain Models.

In nature, some processes are intrinsically random. The most known example is in quantum physics where the quantities that define a particle are random and cannot be known precisely, even with better models and sensors. It is also true to more macroscopic phenomena, where we are unable to model, with full details and variables, phenomenon such as the weather or the traffic of customers in a given store. Uncertainty comes from either approximative models, imprecise measurement by sensors, or approximate calculations. This is where stochastic models come into play, to provide a framework to model with uncertainty

Deterministic models offer clear, precise predictions based on known data, making them reliable in scenarios where events follow set patterns, like in engineering designs or certain scientific experiments. They're great when things are predictable, but struggle with randomness. On the flip side, stochastic models embrace uncertainty, like forecasting stock market fluctuations or unpredictable weather. They're versatile in capturing randomness but might not pinpoint specific outcomes. While deterministic models assure accuracy in predictable settings, stochastic models excel in handling randomness, providing a broader understanding of uncertain scenarios.

Deterministic models normally can give you a clear explanation on why you get this result. You can clearly calculate risk factors an sensitivity to them. However, you can find youself in position that your underlying assumption is just wrong. For instance, 30 years ago interest rate models could easily assume the interest rate is always positive, and some did fail whe market moved in nagative rate territory.

Deterministic models in computer science offer predictability and simplicity, yielding consistent results with the same inputs and being easier to understand. However, they can oversimplify complex systems and become computationally heavy in large-scale applications. Stochastic models, conversely, excel in handling the unpredictability of real-world environments and complex systems with inherent randomness. They are more scalable in uncertain contexts but come with the drawbacks of less predictable outcomes and a need for more complex analysis and larger data sets. The choice between these models depends on the specific context and the balance between the need for predictability and the ability to handle complexity and uncertainty.

In geosciences deterministic models are wrong (and most often very wrong) but simpler to use and present. Stochastic modeling is more complex to use and present but has more chances of providing a reasonable results range, though only if the full range of uncertain parameters is correctly understood.

Deterministic models are generally more simple to implement and to interpret by most. However, they lack the ability to model the various situations that can happen. An exemple is sales forecasting. Deterministic models can be implemented simply in Excel, but the result is of little help to make accurate decisions. In a way or another, you have to anticipate various scenarios. Stochastic models do precisely this, in a sound way. Therefore, they lead to much better decisions. Verifying their accuracy requires to adopt a statistical view of the tests, which can be difficult to some.

To my understand, Deterministic models yield consistent outcomes from given inputs, with no randomness. For example, Newton's laws precisely predict motion if initial conditions and forces are known. They're simple and predictable, suited for systems with fixed rules. Stochastic models incorporate randomness, offering probable outcomes instead of exact predictions. A typical example is weather forecasting, where predictions include probabilities (like a 60% chance of rain) due to inherent atmospheric unpredictability. These models are used for complex systems where uncertainty is a key factor. In essence, deterministic models are used for predictable, rule-based systems, while stochastic models handle uncertain, variable systems.

Deterministic models find their footing in scenarios where outcomes can be precisely predicted, such as in engineering for designing bridges or in physics for calculating motion. On the other hand, stochastic models shine in dealing with randomness, seen in stock market predictions, genetic evolution, or even in simulating traffic flow. Imagine using deterministic models to design a stable bridge or stochastic models to estimate the traffic flow during rush hour. Each excels in different situations, offering valuable insights into how things work, whether in the world of building structures or understanding unpredictable systems like financial markets and genetics.

Deciding between deterministic and stochastic models boils down to the nature of what you're trying to predict. If you're dealing with fixed patterns or known data, deterministic models, like mapping out a clear path, might be your best bet. However, if randomness or uncertainty plays a significant role, stochastic models, resembling a variety of potential paths, could be more fitting. For instance, predicting stable structures might lean towards deterministic models, while understanding unpredictable markets or genetic evolution might favor stochastic ones. It's like choosing the right tool for the job, depending on whether you're dealing with a straightforward path or a complex maze of possibilities.

Deterministic models are based on precise inputs and produce the same output for a given set of inputs. These models assume that the future can be predicted with certainty based on the current state. On the other hand, stochastic models incorporate randomness and uncertainty into the modeling process.

In geosciences the best modeling strategy is always and invariably the stochastic approach given that the deterministic approach only gives wrong results. However uncertainty modeling should not be made in a more complicated way than it needs to be. If the problem is correctly understood it is often sufficient to take into account only the most impacting parameters, following a sensitivity analysis or reasoning (in which it should not however not be forgotten that a combination of parameters can have more impact than the simple addition of the impacts of each parameter)

Physical/chemical systems are analytical, and the relation between variables make the system predictable and deterministic. Any mechanical system , even with nonlinear behaviour is bound in a limit space of solution which hints its repeatability, thus its determinism. Stock market, cash-flow are on the other hand examples of systems which have either under-determination in terms of lack of variables observability, many variables that the modeller can count and by that have hidden variables which will still influe on the system, but which cannot be detected (external to the modelled system), or otherwise totally random behaviour (trust of the buyers, change of a company CEO,...).

In most real life situations, stochastic models provide better results. However, the team in charge may feel uncomfortable with using them and would prefer deterministic models. In the end, the decision should be based on value added. The best model is the one that adds more value to the topics it is applied upon.

In an uncertain world, a deterministic model will be precise but not accurate, and a stochastic model will have a low accuracy and low precision but define the range of outcomes. A good stochastic model is without bias created by either the modeling method or input data. A stochastic modeling tool can be evaluated by looking at the quality of the predicted range once the forecast becomes reality. If the series of actual values are not in the expected ranges or with a consistent offset vis-a-vis the range mean, the model is wrong or biased.

No matter what type of model you choose, you need to manage model risk. Understanding applicability, boundary condition and how to make consistent changes as the model develops, are key. Without those, the best models of today become the worst failures of tomorrow.

The key difference between deterministic and stochastic models is that while a stochastic algorithm recognizes the random nature of input components, the deterministic model does not contain any randomness. In a deterministic model we get an output when we obtain a set of fixed inputs and the relationships between them. On the other hand, when using a stochastic model, since the output is random, it only represents a snapshot of input-output relations at a particular point in time.

For geosciences applications deterministic modeling is the least advisable way to go. However stochastic modeling should not be a substitute for correctly analyzing the data and building a representative model, as is unfortunately often observed. But conversely it may be preferable to build a range of more simple models encompassing the perceived uncertainty on models and parameters rather than ultra-sophisticated models trying to represent everything, as the more sophisticated the model is the more time consuming the task is and the narrower the model adaptability tends to be. Experience - and in my view certainly not AI! - is the key to get it (a bit) right.

Every person in charge of a real life process should consider learning and understanding stochastic models. This would open a whole new way of thinking, providing many useful ideas and results.